Exponential Factor Research Articles

Logistic Map and Exponential Scaling Factor-Based Differential Evolution

Differential evolution (DE), an important evolutionary technique, enhances its parameters such as, initialization of population, mutation, crossover etc. to resolve realistic optimization issues. This work represents a modified differential evolution algorithm by using the idea of exponential scale factor and logistic map in order to address the slow convergence rate, and to keep a very good equilibrium linking exploration and exploitation. Modification is done in two ways: (i) Initialization of population and (ii) Scaling factor.The proposed algorithm is validated with the aid of a 13 different benchmark functions taking from the literature, also the outcomes are compared along with 7 different popular state of art algorithms. Further, performance of the modified algorithm is simulated on 3 realistic engineering problems. Also compared with 8 recent optimizer techniques. Again from number of function evaluations it is clear that the proposed algorithm converses more quickly than the other existing algorithms.

Experimental study and numerical validation of oxy-ammonia combustion at elevated temperatures and pressures

The combustion of fossil fuels, which are mostly based on hydrocarbon chains, produces large quantities of carbon dioxide which is a major contributor to the global warming. Due to alarming concerns, initiatives are taken to promote the use of 'zero-carbon fuel’. The use of ammonia as an alternative fuel in combustors like gas turbines and spark-ignition engines have already been tested. As high pressures and temperatures are encountered in these combustors, it is essential to find laminar flame speed data for ammonia combustion at these conditions. The present study focuses on performing experiments at elevated conditions for different equivalence ratios in a constant volume spherical chamber. A literature study was performed to select and evaluate the most recent kinetic mechanisms for ammonia combustion under these conditions. A sensitivity analysis highlighting the key reactions for two of the schemes has been performed. A range of exponential factors for temperature and pressure which is used to calculate the flame speeds for a given reference conditions : α and β have been determined.

A review of spectral analysis of magnetic data for depth estimation

Spectral analysis has been used for studying a variety of geologic structures and processes, such as estimation of the depth to the crystalline basement or estimation of the Curie temperature isotherm from magnetic anomalies. However, the analysis is not standard because it refers to different theoretical frameworks, such as statistical ensembles of homogeneous sources and uncorrelated or fractal randomly distributed sources. We have aimed to unify the approaches by reformulating all of the common spectral expressions in the form of a product between a depth-dependent exponential factor and a factor, which we call the spectral correction factor, that incorporates all of the a priori assumptions for each method. This type of organization might be useful for practitioners to quickly select the most appropriate method for a given study area. We also establish a new formula for extending the Spector and Grant method to the centroid depth estimation. Practical constraints on the depth estimation and intrinsic assumptions/limitations of the different approaches are examined by generating synthetic data of homogeneous ensemble sources as well as random and fractal models. We address the statistical uncertainty of depth estimates using ordinary error propagation on the spectral slope. Critical parameters, such as the window size, are also analyzed in terms of the type of method used and the geologic complexity. We find that the window size is smaller for the centroid/modified centroid methods and larger for the spectral peak, defractal, and nonlinear parameter depth estimation methods. In any case, the window size can be large in tectonically stable regions and relatively small over volcanically, tectonically, and geothermally active areas. Finally, we estimate and discuss the depth to the magnetic top and bottom in the Adriatic Sea region (eastern Italy) in the context of the heat flow, Moho depth, and gravity data of the region.

Optimal series expansion method for bound states of quantum systems

An optimal series expansion method is developed to improve variational wave functions for the bound state calculation of quantum systems. With one variational parameter residing in the exponential decay factor, the finite power series expansion of the remaining factor in the trial wave function is determined with the criterion that the Schrödinger equation be satisfied as well as possible. In this way, more and more accurate trial wave functions can be obtained without undesirably increasing the number of variational parameters. Thus, instead of the standard variational principle of minimizing the energy expectation value, we utilize an alternative variational principle with which one minimizes the deviation of the trial wave function from being a true eigenstate of the Hamiltonian. The variational principle applies to both the ground state and the excited states. We then employ the optimal series expansion method to calculate the bound states of several quantum systems, including the one-dimensional double well potential, the Morse oscillator, the two-dimensional double well potential, and the vibrational states in the lowest electronic surface of methyl iodide. Computational results indicate that this method can yield excellent results for both energy eigenvalues and eigenfunctions. Therefore, the optimal series expansion method provides an alternative approach to the bound state calculation of quantum systems.

Exponentially correlated Hylleraas‐configuration interaction studies of atomic systems. II. Non‐relativistic energies of the 1 through 6 states of the Li+ ion

AbstractThe exponentially correlated Hylleraas‐configuration interaction wave function (E‐Hy‐CI) is a generalization of the Hylleraas‐configuration interaction (Hy‐CI) in which the single of an Hy‐CI wave function is generalized to the generic type . This type of correlation has the right behavior both in the vicinity of the cusp and as goes to infinity; this work shows that wave functions containing both linear and exponential factors converge more rapidly than either one alone for low‐lying excited states of 1S symmetry. E‐Hy‐CI variational calculations with up to 8568 configurations lead to a nonrelativistic energy of −7.2799 1341 2669 3059 6491 6759 hartree for the 1 1S ground state of the Li+ ion.

A Comparative Study of Multiple Regression and Machine Learning Techniques for Prediction of Nanofluid Heat Transfer

Abstract The aim of this article is to introduce and discuss prediction power of the multiple regression technique, artificial neural network (ANN), and adaptive neuro-fuzzy interface system (ANFIS) methods for predicting the forced convection heat transfer characteristics of a turbulent nanofluid flow in a pipe. Water and Al2O3 mixture is used as the nanofluid. Utilizing fluent software, numerical computations were performed with volume fraction ranging between 0.3% and 5%, particle diameter ranging between 20 and 140 nm, and Reynolds number ranging between 7000 and 21,000. Based on the computationally obtained results, a correlation is developed for the Nusselt number using the multiple regression method. Also, based on the computational fluid dynamics results, different ANN architectures with different number of neurons in the hidden layers and several training algorithms (Levenberg–Marquardt, Bayesian regularization, scaled conjugate gradient) are tested to find the best ANN architecture. In addition, ANFIS is also used to predict the Nusselt number. In the ANFIS, number of clusters, exponential factor, and membership function (MF) type are optimized. The results obtained from multiple regression correlation, ANN, and ANFIS were compared. According to the obtained results, ANFIS is a powerful tool with a R2 of 0.9987 for predictions.

Dynamic Behavior Study of Functionally Graded Porous Nanoplates

This paper introduces the analytical solutions of complex behavior analysis utilizing high-order shear deformation plate theory of functionally graded FGM nano-plate content consisting of a mixture of metal and ceramics with porosity. To incorporate the small-scale effect, the non-local principle of elasticity is used. The impact of variance of material properties such as thickness-length ratio, aspect ratio, power-law exponent and porosity factor on natural frequencies of FG nano-plate is examined. Compared to those achieved from other researchers, the latest solutions are. Using the simulated displacements theory, equilibrium equations are obtained. Current solutions of the dimensionless frequency are compared with those of the finite element method. The effect of geometry, material variations of nonlocal FG nano-plates and the porosity factor on their natural frequencies are investigated in this review. The results are in good agreement with those of the literature.

BER performance of unmanned aerial vehicle assisted spatial modulation system in Rician channels

Unmanned aerial vehicle (UAV) is an emerging technology with high mobility and flexible reconfiguration. In this paper, an UAV-assisted spatial modulation (SM) system with amplify-and-forward (AF) protocol is presented, and the corresponding bit error rate (BER) performance is investigated over Rician fading channels, where the UAV is employed as a half-duplex relay and remains stationary over a given area, and the path loss exponent and Rician factor depend on the position of the UAV. Based on the imperfect channel state information (CSI), the effective signal-to-noise ratio (SNR) of the system is firstly derived. Then, with this result, we analyze the BER performance of the system, and deduce an upper bound of average BER for evaluation. On these bases, the asymptotic performance under large SNR is analyzed, and asymptotic expression of BER bound is derived to attain the diversity gain which is zero for imperfect CSI and one for perfect CSI. Simulation results demonstrate the effectiveness of the presented performance analysis, and reveal that the degradation arisen from estimation error and multiple antennas at the transmitter in BER performance is serious while the improvement brought by spatial diversity at the receiver is relatively modest. Specifically, the increase of 0.04 in estimation error variance results in the diminution of 12.5dB in performance gain, and the use of eight transmit antennas is 8dB worse than two transmit antennas. At the receiver, the increase in performance gain offered by going from ND=1 to ND=6 is about 4dB. Furthermore, according to the simulation, the optimal BER performance can be reached by adjusting the UAV position and power allocation factor. At last, the open issues and challenges focusing on both the deployment and architecture of this system are highlighted.

Quality factor of partially coherent Airy beams in a turbulent atmosphere.

The quality factor of a partially coherent Airy beam in a turbulent atmosphere is investigated with the help of the extended Huygens-Fresnel integral formula and the Wigner distribution. From the numerical results, based on the analytical formula, we find that increasing the inner scale or decreasing the structure constant of the refractive index fluctuations of the turbulent atmosphere tends to decrease the quality factor of a partially coherent Airy beam in a turbulent atmosphere. Moreover, it is found that increasing the scale factor and wavelength or decreasing the coherent length of a partially coherent Airy beam can also be used to decrease the quality factor of a partially coherent Airy beam in a turbulent atmosphere. However, the quality factor of a partially coherent Airy beam in a turbulent atmosphere has a maximum when the exponential truncation factor of a partially coherent Airy beam is 0.63. Our results will be useful in long-distance free-space optical communications and laser defense.

Surface effect on size dependent Young’s modulus of nanowires: Exponentially decreased surface elasticity model

Physical and mechanical properties of nanowires are strongly affected by surface effects. In this letter, a continuum theoretical scheme for describing the elastic property of nanowires was proposed. The influence of surface elasticity was considered as a decreasing regular pattern with increasing distance from surface. The decrease law was considered as exponential in this letter. An imaginary interface (between bulk like core and surface area) of nanowires appears in core-surface and core–shell models. This theoretical model avoided the non-physical interface between bulk like core and surface area of nanowires. The larger exponential decrease factor weakened surface effect obviously and was reflected in the effective Young’s modulus expression. Due to the influence of descending surface elasticity, the second, third, fourth and fifth surface modifications were introduced. This letter is aim to establish a continuum theory for elastic property of nanowires without any sudden change (interface) of Young’s modulus.

Size and Temperature Effect on Electrical Conductivity, Dielectric Properties, and Electrical Switching Memory Application of Nanocrystalline Na-DDQ (Metal-Organic Frameworks) Thin Films

Organometallic Sodium-2,3-Dichloro-5,6-dicyano-p-benzoquinone (Na-DDQ) films were synthesized using a conventional thermal vacuum deposition technique at ambient temperature. DC electrical resistivity was measured over a wide range of thicknesses and temperatures. This helps in investigating the different size-effect parameters, for instance the bulk mean free path (λ o ), bulk resistivity (ρ o ), grain-boundary transmission coefficient (t), surface scattering factor (p), external surface parameters (U), and grain-boundary parameter (V) in specular and non-specular conditions. The contribution of grain-boundary and surface resistivity to total resistivity was then estimated. Additionally, the AC conductivity (σ ac ) and dielectric (ε) behavior of Na-DDQ films were examined at the same temperature in the frequency range (50 Hz-5 MHz). Thus, the temperature dependence of frequency exponent factor (s) was calculated and interpreted in terms of various conduction models. The AC activation energy and its frequency dependence were extracted. The dielectric properties were attributed using electric modulus and complex permittivity of the studied films. Finally, Na-DDQ films showed a memory and switching behavior during the I–V characterization, the On-Off states were observed by applying an external electric field. Hence, the switching parameters for instance threshold voltage (Vth), switching time (τ s) and delay time (τ d) of samples were evaluated.

난류생성기 판 형상에 의한 난류화염 특성 연구

The cross-shaped fractal grids which have RRBT(reduced ratio of bar thickness) and the hexagonal grid were used to generate various turbulent flow properties for low swirl flames. In the non-reacting flow field with the fixed bulk velocity at 10 m/s, decreasing RRBT induces the increasing turbulent intensity(ISUBU/SUB) with the delay in the location of lowest turbulent mean velocity(Ū) and highest turbulent fluctuation(ú) due to vortex shedding from the bar thickness. This phenomenon was well explained by a wake interaction theory using axial velocity profiles at the centerline. At various equivalence ratios for Hexa. and fractal grids, the characteristics of low swirl flames could be identified to a thin reaction zone regime in the Borghi – Peter regime diagram. Decreasing RRBT increases ISUBU/SUB in front of flame brush with increasing turbulent local displacement speeds (SSUBT,LD/SUB) via a linear correlation. The turbulent Reynolds number, ReSUBT/SUB composed of the ratio of length scale and velocity components induced the proportional trends in non linear relationship showing that the influence of the length scale ratio. The empirical correlation study of SSUBT,LD/SUB as a function of ReSUBT/SUB and ú/SSUP0/SUPSUBL/SUB was investigated to compare the influence of velocity and turbulent length scales ratio. The result of linear correlation equation with SSUBT,LD/SUB indicates the influence of velocity factors greater than ReSUBT/SUB through the exponential factor.

ПАРАМЕТРИ НЕВ’ЯЗКИ АПРОКСИМАЦІЙ ДИСКРЕТНО ЗАДАНИХ ЗАЛЕЖНОСТЕЙ АНАЛІТИЧНИМИ ФУНКЦІЯМИ ТА КРИТЕРІЇ ПОШУКУ ОПТИМАЛЬНИХ ЗНАЧЕНЬ ЇХНІХ КОЕФІЦІЄНТІВ

Universal discrepancy parameters of approximations of discretely specified dependencies by analytical functions and search criteria for optimal values of their coefficients, as well as analysis of features of their application are described. Discrepancy parameters of approximations, which do not depend on the ranges of variation of the values of functions and the number of points of a discretely specified dependence, are proposed. They can be effective for objectively comparing the quality of approximations of any dependencies by any functions. Approximations of a discretely specified dependence of the mathematical expectation of the equivalent electrical resistance of a layer of aluminum granules during spark-erosion dispersion in water on the instantaneous values of the discharge current are carried out. As approximating functions, we chose a power function with an exponent factor –1 and a function based on exponential. Using the criteria of the least approximation error, the optimal values of the coefficients of both approximating functions are founded. It is shown in which cases it is advisable to use the combined search criteria for the optimal values of the coefficients of the approximating functions, and in which are enough simple one-component ones. Ref. 27, fig. 2, tables 2.

A dynamic flotation model for predictive control incorporating froth physics. Part I: Model development

It is widely accepted that the implementation of model-based predictive controllers (MPC) ensures optimal operation if an accurate model of the process is available. In the case of froth flotation, modelling for control purposes is a challenging task due to inherent process instabilities. Most models for control have only focused on the pulp phase rather than the froth phase, which is usually oversimplified or even neglected. Despite the fact that froth stability can significantly affect the overall performance of flotation cells, there is still a gap in literature regarding flotation models for control purposes that properly include froth physics.In this paper we describe the development of a dynamic flotation model suitable for model predictive control, incorporating equations that describe the physics of flotation froths. Unlike other flotation models for control in the literature, the model proposed here includes important variables related to froth stability, such as bursting rate and air recovery, as well as simplified equations to calculate froth recovery and entrainment. These model equations allow estimating the amount of valuable material reporting to the concentrate, which can be used as a proxy to estimate grade and recovery. Additionally, pulp-froth interface physics was also included in our model, which enables a more accurate prediction of relevant flotation variables.A sensitivity analysis of the parameters showed that two out of seven parameters were highly sensitive. The highly sensitive parameters are the exponential factor n of the equation for the overflowing bubble size, and the constant value a of the equation for the bursting rate. Although the other parameters showed a reasonably lower sensitivity than n and a, the results also revealed that there is a significant difference in the prediction accuracy if the parameters are poorly estimated. Further simulations of important variables for control exhibited a good adaptability to changes in typical variables, such as air and feed flowrates.An analysis of degrees of freedom of the model established that two variables need to be fixed to have a completely determined system. This means that two variables are available for control purposes, which can be air and tailings flowrates (through the manipulation of the respective control valves). This study therefore paves the way for the implementation of a robust dynamic model for flotation predictive control, incorporating important froth phenomena.

Optimal Liquidation Behaviour Analysis for Stochastic Linear and Nonlinear Systems of Self-Exciting Model with Decay

When the market environment changes, we extend the self-exciting price impact model and further analysis of investors’ liquidation behaviour. It is assumed that the model is accompanied by an exponential decay factor when the temporary impact and its coefficient are linear and nonlinear. Using the optimal control method, we obtain that the optimal liquidation behaviours satisfy the second-order nonlinear ODEs with variable coefficients in the case of linear and nonlinear temporary impact. Next, we solve the ODEs and get the form of the investors’ optimal liquidation behaviour in four cases. Furthermore, we prove the decreasing properties of the optimal liquidation behaviour under the linear temporary impact. Through numerical simulation, we further explain the influence of the changed parameters ρ , a , b , x , and α on the investors’ liquidation strategy X t in twelve scenarios. Some interesting properties have been found.

Modified Archie\u2019s parameters for estimating water saturation for carbonate reservoir in north of Iraq

Archie’s parameters, cementation factor (m), saturation exponent (n) and tortuosity factor (a), are general factor that have effects on water saturation magnitude, due to their sensitivity to pores distribution, lithofacies properties and wettability, particularly in carbonate reservoirs. Water saturation magnitude has a direct effect in estimating initial oil-in-place values, and inaccuracy in its values will lead to huge impact errors in initial oil-in-place values, so it would affect the economics of field management and development plans. In this paper, the main objective was to investigate the impact of using conventional and modified Archie’s parameters in the determination of water saturation from well log interpretation for Tertiary reservoir in Khabaz oil field, a heterogenous carbonite reservoir in the north of Iraq which was affected by different digenesis processes that impacted the reservoir quality. Tertiary reservoir of Khabaz field consists of five geological units (A, B, C, D and E), and the selected well penetrated the top of the reservoir at 2200.5 m RTKB and passed through five geological units and reached total depth at 2348 m RTKB. The geothermal gradient of the field was 1.12 ℉ per 100 ft, and formation water resistivity (Rw) was about 0.029 Ω m. Water saturation was at first estimated from resistivity logs by Archie model with conventional known values of parameters (a, m and n) (1, 2 and 2), respectively, and then Archie’s parameters were modified and determined by graphical technique of Pickett plot for each geological unit to estimate water saturation. Finally, the results show the water saturation value was more sensitive for Archie’s parameter in low-porosity and high-clay-volume zone, but less sensitive in clean high-porosity zone, and water saturation values determined by modified Archie model were less about 18.5% at mean than their value by using conventional Archie’s parameters.

Preparation and pyrolysis kinetics of melamine phytates/rigid polyurethane foam composites

A series of melamine phytates/rigid polyurethane foam (MEL-PA/RPUF) composites were prepared by one-step water-blown method with MEL-PA as flame retardant. Thermogravimetric analysis (TG) and thermal analysis kinetics were used to study the thermal stability of the composites and reveal its degradation mechanism. The results show that the char residues of MEL-PA/RPUF gradually increases at 700℃ with the increase of MEL-PA loading. Based on TGA data, the reaction grade n, activation energy E and pre exponential factor A of the main degradation stage for the composites were calculated by the Coats-Redfern and Horowitz-Metzger integration methods. The results show that MEL-PA promotes the initial degradation of the composites in air atmosphere, while the MEL-PA/RPUF composites have higher thermal stability in the high temperature stage, and the two calculation methods have the same law. In N2 atmosphere, MEL-PA30/RPUF (mass fraction of MEL-PA is 10.3wt%) has higher n and E compared with RPUF. The results indicate that the reaction of MEL-PA30/RPUF is more complex and the thermal stability is higher. The mathematical model and experimental analysis by Criado method verify the feasibility of the Coats-Redfern method. The results of thermal degradation kinetics of MEL-PA/RPUF composites provide reference for the analysis of flame retardation performance of RPUF with different flame retardation systems.

Density peak clustering using global and local consistency adjustable manifold distance

A novel density-based clustering algorithm, called Density Peak Clustering (DPC), has recently received great attention due to its efficiency in clustering performance and simplicity in implementation. However, empirical studies have demonstrated that the commonly used distance measures in DPC cannot simultaneously consider global and local consistency, which can cause the estimated local densities based on it incapable of capturing the ground-truth data structure and thus produce poor clustering results, especially when the clusters existing in datasets exhibit multi-density manifold structures characteristics with different sizes. In order to address those limitations, we propose a novel density peak clustering algorithm using global and local consistency adjustable manifold distance in this paper. In the proposed algorithm, a novel manifold distance with exponential term and scaling factor is introduced to estimate local densities of all data points. By modifying its exponential term and scaling factor, we can flexibly adjust the ratio of the distance between the data within the same manifold to the distance between the data across different manifolds. This flexible adjustment is beneficial to the estimated local densities more accurately reflecting the global and local consistency of data structures. In addition, to effectively deal with clusters with different densities and sizes, a compensation strategy for distance from nearest point with larger density, called local-scale tuning distance, is developed for our proposed approach. By the developed local-scale tuning distance, underlying cluster centers of clusters with different densities and sizes, especially the clusters with low densities or small sizes can remarkably stand out from the decision graph so that the proposed method can accurately identify the number of underlying clusters in the decision graph and thus obtain satisfactory clustering results. In the experimental part, the effect of the scaling factor on the performance of the proposed technique is discussed and some suggestions about the determination of the parameters are given. Theoretical analysis and experimental results on several synthetic datasets and read-world datasets demonstrate that the proposed approach is superior to other existing clustering techniques in terms of three evaluation metrics with statistical significance.

Thermal degradation kinetics of ethyl vanillin crosslinked chitosan/poly(vinyl alcohol) blend films for food packaging applications

The precise knowledge of thermal degradation of polymers appears to be of great importance in order to identify their applications. In the present work ethyl vanillin (EV) cross linked chitosan (CS)/poly(vinyl alcohol) (PVA) (CPEV) blend films of different mass percent were prepared by solvent casting method, and were characterized by using thermogravimetric/derivative thermogravimetric (TG/DrTG), differential scanning calorimetry (DSC) and X-ray diffraction (XRD) techniques. Non-isothermal (dynamic) thermogravimetry was used with three different heating rates (β) namely 5.0, 7.5 and 10.0∘Cmin−1 Kinetic parameters such as activation energy (Ea) and pre exponential factor (A) were calculated using Flynn-Wall-Ozawa (FWO) equation, Kissinger-Akahira-Sunose (KAS) equation and Kissinger relation at three different stages of thermal degradation. The improved thermal staCDC100739ility of EV crosslinked blend films could be due to the formation of Schiff base and inter molecular hydrogen bonding. Calculated percentage of crystallinity (X%) results from DSC and XRD data found to be in good agreement with each other. Crystallinity decreased with increase of CS percent in CPEV blend films.

Thermal Residual Stress and Failure Probability of Functionally Grade Ni-YSZ Anode of Solid Oxide Fuel Cells Using a Finite Element Analysis

Due to the differences of thermal expansion coefficient between the components in the solid oxide fuel cells (SOFCs), there is a large residual thermal stress in the fabrication process of the cell. In this study, the functionally graded (FG) Ni-YSZ anode design was introduced between Ni-YSZ support and YSZ electrolyte to mitigate the thermal residual stress in SOFC. In the current FG anode design, composition of Ni and YSZ was varied according the function of φ (Ni) = k ( t / H ) n , where k is a constant which is equal to the volume fraction of Ni in Ni-YSZ anode support layer, t is the distance to the electrolyte, H is the thickness of the FG anode layer and n is the exponential factor. In the numerical model, the FG anode layer was evenly divided into m sublayers. The porosity was set to a constant value of 0.3 and uniformly distributed in the anode. The residual stress of the anode was modeled as the thermal stress when the anode was cooled from the reduction temperature of 1200 oC to room temperature of 20 oC. Residual thermal stress was calculated by finite element method (FEM) using the commercial ANSYS package. Failure probability of functionally graded SOFC was evaluated using the classic Weibull probability model.The effects of sublayer number m = (1, 2, 3, 4), exponential factor n = (0.25, 0.5, ..., 4.0) and gradient layer thickness H = (20, 30, 40 μm) on the stress and failure probability of functionally graded SOFC are discussed. The calculation results show that the FG anode layer can obviously reduce the stress, and effectively decrease the stress concentration between electrode and electrolyte. The failure probability can be reduced by two orders of magnitude at most as compared with the conventional SOFC. Under the same exponential factor n , appropriately increasing the number of sublayers m can reduce the stress of the gradient layer. The sublayers number m = 2 is a suitable value. With the increase of the thickness of the gradient layer, the anode failure probability increases. The research provides a reference for further optimizing the stress in SOFC.