Muller Method Research Articles

Effect of Flow Discharge on Sedimentation in Paneki River

Introduction: Paneki River has the potential for sedimentation caused by flow discharge. The condition of the river is getting wider every day which will threaten the risk of flooding if there is heavy rain with high intensity. The purpose of this study is to determine the return time flood discharge and basic sediment transport discharge in the Paneki river which can be used as a reference in planning sediment control buildings. Method: This research method includes primary data collection and secondary data collection, data management including calculating width, slope, design rainfall, design flood discharge, sieve analysis, and specific gravity. Then proceed to calculate the return time flood discharge using the Nakayasu synthetic unit hydrograph method and basic sediment transport using the Meyer-Peter and Muller method. Results and Discussion: From this research, the result of the 2-year return time flood discharge is 121.306 m3/det, for 5-year return time flood discharge is 185.069 m3 /det, for 10-year return time flood discharge is 209.261 m3 /det, for 25-year return time flood discharge is 312.359 m3 /det, and for 50-year return time flood discharge is 373.566 m3 /det. The results of basic sediment transport discharge per cross-section ranged from 0.0000861 m3 /det to 0.005641775 m3 /det. Conclusion: The study shows that sedimentation is influenced by flow discharge. The results of the calculation of flow discharge (Q) and bottom sediment transport (Qs) in Paneki River using the Meyer-Peter and Muller method resulted in Qs varying from 0.0000861 m³/det to 0.016551197 m³/det, according to the measured flow discharge. The greater the flow discharge, the greater the sediment transport, indicating a direct relationship between flow discharge and sedimentation.

Analysis of natural vibration of truncated conical shells partially filled with fluid

AbstractIn this paper, we study the vibrational behavior of shells in the form of truncated cones containing an ideal compressible fluid. The sloshing effect on the free surface of the fluid is neglected. The dynamic behavior of the elastic structure is investigated based on the classical shell theory, the constitutive relations of which represent a system of ordinary differential equations written for new unknowns. Small fluid vibrations are described in terms of acoustic approximation using the wave equation for hydrodynamic pressure written in spherical coordinates. Its transformation into the system of ordinary differential equations is carried out by applying the generalized differential quadrature method. The formulated boundary value problem is solved by Godunov's orthogonal sweep method. Natural frequencies of shell vibrations are calculated using the stepwise procedure and the Muller method. The accuracy and reliability of the obtained results are estimated by making a comparison with the known numerical and analytical solutions. The dependencies of the lowest frequency on the fluid level and cone angle of shells under different combinations of boundary conditions (simply supported, rigidly clamped, and cantilevered shells) have been studied comprehensively. For conical straight and inverted shells, a numerical analysis has been performed to estimate the possibility of finding configurations at which the lowest natural frequencies exceed the corresponding values of the equivalent cylindrical shell.

Multi-Objective Profit-Based Unit Commitment with Renewable Energy and Energy Storage Units Using a Modified Optimization Method

The unit commitment (UC) problem aims to reduce the power generation costs of power generation units in the traditional power system structure. However, under the current arrangement, the problem of cutting the cost of producing electricity has turned into an opportunity to boost power generation units’ profits. Emission concerns are now given considerable weight when talking about the performance planning of power generation units, in addition to economic objectives. Because emissions are viewed as a limitation rather than an objective function in the majority of recent research that has been published in the literature, this paper solves the multi-objective profit-based unit commitment (PBUC) problem while taking into account energy storage systems (ESSs) and renewable energy systems (RESs) in the presence of uncertainty sources, such as demand and energy prices, in order to minimize generated emissions and maximize profits by power generation units in the fiercely competitive energy market. Owing to the intricacy of the optimization problem, a novel mutation-based modified version of the shuffled frog leaping algorithm (SFLA) is suggested as a way to get around the PBUC problem’s difficulty. A 10-unit test system is used for the simulation, which is run for a whole day to demonstrate the effectiveness of the suggested approach. The proposed algorithm’s output is compared with the best-known approaches from various references. The simulated results generated by the suggested algorithms and the previously reported algorithms to solve the PBUC problem show that the proposed method is better than other evolutionary methods utilized in this study and prior investigations. For example, the overall profit from the suggested MSFLA is around 4% and 5.5% higher than that from other algorithms like the ICA and Muller methods in the presence and absence of reserve allocation, respectively. Furthermore, the MSFLA emissions value is approximately 2% and 8% lower than the optimum emissions values obtained using the PSO and ICA approaches, respectively.

Video Deepfake classification using particle swarm optimization-based evolving ensemble models

The recent breakthrough of deep learning based generative models has led to the escalated generation of photo-realistic synthetic videos with significant visual quality. Automated reliable detection of such forged videos requires the extraction of fine-grained discriminative spatial-temporal cues. To tackle such challenges, we propose weighted and evolving ensemble models comprising 3D Convolutional Neural Networks (CNNs) and CNN-Recurrent Neural Networks (RNNs) with Particle Swarm Optimization (PSO) based network topology and hyper-parameter optimization for video authenticity classification. A new PSO algorithm is proposed, which embeds Muller's method and fixed-point iteration based leader enhancement, reinforcement learning-based optimal search action selection, a petal spiral simulated search mechanism, and cross-breed elite signal generation based on adaptive geometric surfaces. The PSO variant optimizes the RNN topologies in CNN-RNN, as well as key learning configurations of 3D CNNs, with the attempt to extract effective discriminative spatial-temporal cues. Both weighted and evolving ensemble strategies are used for ensemble formulation with aforementioned optimized networks as base classifiers. In particular, the proposed PSO algorithm is used to identify optimal subsets of optimized base networks for dynamic ensemble generation to balance between ensemble complexity and performance. Evaluated using several well-known synthetic video datasets, our approach outperforms existing studies and various ensemble models devised by other search methods with statistical significance for video authenticity classification. The proposed PSO model also illustrates statistical superiority over a number of search methods for solving optimization problems pertaining to a variety of artificial landscapes with diverse geometrical layouts.

Nonlinear excitation and mesh characteristics model for spiral bevel gears

Accurate and rapid calculation of nonlinear excitation (NE) and loaded mesh characteristics (LMC) of gear pairs is a key to achieving rapid iterative optimization of gear system designs. Therefore, an analytical model (AM) was proposed for the accurate and numerically efficient calculation of NE and LMC for application to spiral bevel gears (SBG). First, a tooth contact analysis of an SBG was completed using Coons surface technology and mesh theory to determine the contact path and unloaded transmission error (UTE). Thus, an AM for the principal and relative normal curvatures of the SBG was derived using the Euler's formula. Based on the traditional calculation method for a Hertz contact ellipse, the relation between the relative curvatures was introduced to derive the formulas for the major and minor axes using the Muller's method, which could improve the programmability and avoid numerical instability of the program. Then, analytical models for the contact ellipse and pressure distribution on the contact tooth surfaces were derived using the Hertz model and geometric theory. Subsequently, based on a single tooth LMC, infinitesimal method, elasticity, and series stiffness model, a single mesh stiffness (SMS) model for SBGs was developed, which incorporates transverse tooth stiffness, transverse gear foundation stiffness, axial tooth stiffness, axial gear foundation stiffness, and Hertz nonlinear contact stiffness. Based on the SMS and UTE, compliance and load matrices were established, and the time-varying mesh stiffness, loaded transmission error, mesh force, and multi-tooth LMC models of the SBG were determined. Finally, the proposed method was validated against nonlinear FE simulations using examples. Compared to FE simulations, the proposed method requires significantly less computational effort and can be further extended to optimization or system analysis problems.

Effect of bed shear stress on the mobile armor layer at the riverbed

Armoring is forming an armor layer of the riverbed which is preceded by the transportation of bed sediment. Mobile armor occurs when the riverbed reaches equilibrium, then eroded, and the surface of the riverbed recovers. Therefore, protection is formed by moving riverbed material. This research used a simulation model generated through HEC RAS software version 6.1. The model input location was Krasak River, Sleman, Yogyakarta. The data for model input were the topography of the Krasak River from upstream to the point of view, flood discharge hydrograph, and grain size gradations. The simulation combination consisted of three locations with the riverbed material of each location sampled tested for grain size distribution. The running simulations combined the flood discharge at return periods of 2, 5, 10, 25, 50, and 100 years. There were three variations of grain size distribution used as input data. Meanwhile, variations of sediment transport methods used the Meyer-Peter Muller and Wilcock-Crowe methods. Overall, the simulation results show that the shear stress and the proportion of sand-to-grain material affect the armoring process and riverbed changes.

Analysis of Sedimentation Rate in the Air Sambat River, Kaur District Using the Meyer Peter Muller and Van Rijn Methods

Analysis Of Sedimentation Rate in The Sambat River Kaur Regency Using Meyer Peter Muller and Van Rijn. The Air Sambat River is located in Maje District, Kaur Regency, Bengkulu Province. The Air Sambat River is a community cultivation area, both in the river border line (GSS) area and in the water catchment area. The condition of the flow of the Air Sambat River is categorized as bad, during the dry season the water can recede drastically, and in the rainy season, it can cause flooding. The data obtained in the field are in the form of flow velocity, depth, and bedload samples. Therefore, this study was conducted to determine the type of sediment and determine the rate of bottom sediment transport in the Lower Air Sambat River in the Air Sambat River, Kaur Regency, Bengkulu Province. Research samples were tested in the laboratory to determine the type of soil and obtain data used for analysis. The analytical calculation method used in this research is the Meyer Peter Muller method and the Van Rijn method. The results showed that the Meyer-Peter Muller method was suitable to be used to describe the conditions of sediment deposition in the review area with a sedimentation rate of 3,057 × 105 tons/year

Snail Slime Extracted by a Cruelty Free Method Preserves Viability and Controls Inflammation Occurrence: A Focus on Fibroblasts.

Snail slime (SS) is a viscous secretion obtained from different snail species. SS composition is variable according to factors such as the extraction method. Even if several papers have been published regarding this topic, the molecular mechanisms at the base of SS biological effects remain unexplored. Thus, the aim of this study is to evaluate the capability of SS, extracted with the cruelty-free Muller method, to promote viability and angiogenesis processes and, in parallel, to counteract inflammation occurrence on skin cell populations. SS was administered to keratinocytes, macrophages and fibroblasts, then cell viability, through 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) test, cytotoxicity by lactate dehydrogenase (LDH) assay, morphology by haematoxylin-eosin staining, gene and protein expression through real-time polymerase chain reaction (PCR) and Western blot, cell cycle phases by flow cytometry, and collagen secretion using an enzyme-linked immunosorbent assay (ELISA) test, were measured. Our results evidence SS capability to promote fibroblast viability and to trigger recovery mechanisms by activating the Erk protein. Moreover, an appreciable anti-inflammatory effect due to the significant reduction in cyclooxygenase-2 expression, and a positive modulation of new blood vessel formation demonstrated by increased Angiopoietin 1 gene expression and a higher matrix deposition (evidenced by the augmented amount of released collagen I) can be identified. This evidence led us to assume that the Muller method extracted-SS represents a valuable and promising natural product suitable for cosmetic and skin care formulations.

Proper normal waves in a two-layer tube taking into account the rheological properties of materials

The article considers the problem of propagation of proper normal waves in a two-layer pipe, paying to attention the rheological properties of the material. The main purpose of the work is to develop a methodology, an algorithm for investigation the problems of wave propagation in extended two-layer dissipatively inhomogeneous cylindrical structures. The main integro-differential equations in the article are obtained on the basis of methods of the theory of visco-elasticity. In the course of the study, the method of separation of variables, the freezing method, the Muller method and the Godunov orthogonal run method were used. In this paper, for structurally inhomogeneous extended cylindrical mechanical systems, the dependences of several modes (three and four) of the complex phase velocity (real and imaginary parts) on the wave number are comparatively estimated; the results of calculations are compared with experimental and theoretical data of other researchers, and the use of asymptotic and numerical methods for solving dispersion equations with complex output parameters is justified.

The natural vibrations of shell structures taking into account dissipative properties and structural heterogeneity

The paper considers the natural oscillations of shell structures. In general, these structures are a set of deformable elements with different rheological properties. An algorithm for solving the viscoelastic dynamic problems has been developed for the complex axisymmetric structures. The physical properties of the viscoelastic structural elements are described by linear Boltzmann-Voltaire relations with integral difference cores. The three-parameter core of Rzhanitsyn-Koltunov was used as the relaxation core. In general, the problem is reduced to solving the systems of first-order ordinary differential equations in the complex variables. A frequency equation is obtained, for the solution where the Muller method is applied. The calculated values of the natural frequencies of oscillations with a given degree of accuracy are given.

Natural waves in a spatial viscoelastic cylinder with a radial crack

The investigation of the dispersion of waves in elastic bodies with different cutouts is of great interest in various scientific and technological fields. The objective of this research is to examine the propagation of free damped waves in elastic dissipative bodies with longitudinal notches. The dynamic behavior of cylindrical bodies with different cutouts is described by the equations of viscoelasticity. The solution of a system of differential equations is expressed by cylindrical Bessel and Hankel functions. The frequency equation is solved using the Muller, Gauss, and orthogonal run methods. It is found that with a decrease in the oscillation frequency in a cylinder of a given radius, the phase and group velocities of the longitudinal wave tend to the common limit - the phase velocity of the rod waves. It is found that as the oscillation frequency reduces in a cylinder of a given radius, the phase and group velocities of the longitudinal wave tend to converge towards the common limit. Additionally, it was found that for a specific value of the Poisson's ratio (0.2833), the frequencies of the shear and radial longitudinal resonances coincide in the cylinder.

Intrinsic oscillations of viscoelastic three-layer truncated conical shell

Conical shells are used in rocket engineering, construction, aircraft engineering and shipbuilding. The purpose of the present work is to carry out a technique, algorithm and programs for obtaining resonant frequencies and waveforms for circular viscoelastic three-layer conical shells. On the basis of the Lagrange variation equation integral-differential equations of own vibrations are obtained. Based on the method of finite elements, a method for solving the problem of eigen-wear oscillations of the truncated three-layer shell with handedly and freely resting edges was carried out. The problem comes down to solving algebraic equations a large order. Obtained a frequency equation with complex output parameters. The proper oscillations of truncated conical shells are investigated, some characteristic features are revealed. Solving the frequency equation by the Muller method, complex roots are determined. It is established that as the elastic modulus of the shell increases, the real and imaginary parts of the natural frequencies increase accordingly. Paying attention to the rheological properties allows you to increase the values of frequency up to 15%.

Nonlinear Vibration Induced by Friction in a Ball Joint System

In this paper, the nonlinear oscillations induced by friction in a ball-on-socket system are investigated. The nonlinear time response was obtained by solving the differential equations of the friction-noise model of the finite element ball with multiple modes. The different patterns of motion were analyzed via the bifurcation diagram, Poincare map, and recurrence plot. The Lyapunov exponents of the discontinuous system with distributed contact were calculated using the Muller method. From the analysis, it is shown that a friction-noise of a ball joint can retain periodic, quasi-periodic, or chaotic oscillations with respect to tilted contact.

A dual porous and fractures medium CBM numerical model development and analysis

The drilling unloading will produce fractures in the plastic zone around the borehole. However, the fracture is the main seepage channel of coalbed methane. It is not appropriate to ignore the influence of fractures on gas flow, especially in the plastic zone. According to the stress redistribution characteristics after unloading, the fracture field in the plastic zone is considered in the coalbed methane numerical model. A two-dimensional random fracture field is introduced via the Monte Carlo method in the plastic zone, which is based on the central limit theory and box muller method. A dual porous and fracture medium numerical model is proposed, which considers not only gas adsorption and desorption, but also fracture distribution and creep deformation. A comparison between the proposed model and the single porous medium numerical model is carried. The results show that the proposed model can reflect not only the evolution characteristics of gas flow but also the anisotropic influence of fracture. It further explains the evolution mechanism and distribution law of gas flow. Finally, the influence of fracture field parameters (fracture density, fracture length, and fracture width) on gas flow is discussed, which is expected to provide a theoretical basis and reference for the development and research of coalbed methane.

Numerical and perturbation solutions for the gauss potential

We will focus on the Schrodinger eigenvalue problem for a Gauss potential in this study. When high and relatively large values of the coupling constant g2 are involved, we will compare eigenvalues E determined numerically with those obtained using the asymptotic series. However, we were interested in the mathematical elements of this comparison throughout the course of this work and explored it for considerably larger, albeit no longer physically plausible, values of g2. Even for power potentials where the Gaussian is a common example, Muller's perturbation method shows some fascinating mathematical characteristics of the Schrodinger equation. The solution's overall analytic features are very similar to well-known periodic differential equations like the Mathieu equation.

Survey and Review

Gaussian (also known as normal) probability distributions in (\mathbb R^d\) play a central role in statistics and are important in many branches of pure and applied mathematics, statistical physics, and several other fields. In the univariate (d=1) case, the corresponding bell curve is known even to many people outside the sciences. At present, there is much interest in algorithms that generate random vectors (X) in (\mathbb R^d) distributed according to a target Gaussian density function. In the scalar (d=1) case, or when (d>1) but the scalar components of (X) are not correlated, there are several simple efficient algorithms, including the well-known Box--Muller method. In the general case, where (d>1) and there are correlations between the scalar components, the standard approach is to perform a linear change of variables (X = LY) so that the components (Y) are uncorrelated and may be sampled easily. Typically, the matrix (L) is obtained via a Cholesky factorization of the precision matrix of the target distribution, an approach which works well if (d) is not too large (for a laptop if, say, (d < 10^5)). However, many recent applications, including image analysis, spatial statistics, graphical structures, and others, operate with very large values of (d) and the Cholesky algorithm, with an (\mathcalO(d^3)) complexity and (\mathcalO(d^2)) memory requirements, may not be feasible. The Survey and Review paper in this issue, “High-Dimensional Gaussian Sampling: A Review and a Unifying Approach Based on a Stochastic Proximal Point Algorithm” by Maxime Vono, Nicolas Dobigeon, and Pierre Chainais, addresses the problem of obtaining Gaussian samples when the Cholesky factorization is not an option. The paper presents in a unified way and compares many algorithms suggested in different scientific communities. The algorithms may be grouped into two classes. In the first, numerical linear algebra techniques are used to reduce the computational complexity and/or the memory requirements. In the second, the samples are obtained via Markov chain Monte Carlo approaches; surprisingly, the resulting algorithms are very much related to classical iterative methods for the solution of linear systems, including Jacobi, Gauss--Seidel, and SOR. For this reason the paper will be relevant to readers interested in numerical linear algebra. For those whose work requires generating random samples, the paper includes a neat decision tree to choose, in a given application, among the many available algorithms. The authors have also made available software for all the methods considered in their survey.

Design of Gaussian modulator for continuous-variable quantum key distribution

The continuous-variable quantum key distribution experimental system requires the randomness and speed of a Gaussian modulator. We present the hardware design for a Gaussian random number (GRN) generator based on the Box–Muller method, which can be implemented on a field-programmable gate array (FPGA). An external high-speed true random number generator application-specific integrated circuit (ASIC) is used to this end. The ASIC operates faster and more independently compared with other Gaussian algorithms based on a linear feedback shift register. The trigonometric and logarithmic functions are calculated using the nonuniform piecewise linear approximation. The calculation of the Gaussian random modulus and phase value is realized using this hardware. Compared with an arbitrary waveform generator, the GRN can be uploaded to a computer to estimate the security key rate. Furthermore, the GRN generator accurately provides a Gaussian probability density function that passes the Jarque–Bera inspection and Lilliefors tests. The proposed FPGA-based system is demonstrated to convert eight-channel 320-Mbps uniform random numbers to 40-MHz 16-bit GRN in real time. Finally, the control of the optical module and Gaussian modulation is realized via the FPGA-based outputs of four dual-channel, 16-bit, 1-giga samples per second digital-to-analog converters.

Propagation of leaky Rayleigh waves along a curved fluid-solid interface.

A characteristic equation is derived for a leaky Rayleigh wave (LRW), propagating on a curved fluid-solid interface. The equations of motion for the curved solid and fluid are formulated using the constitutive equations of a homogenous isotropic curved solid and an inviscid fluid, respectively. The displacement potential functions are used to simplify the derivation. The interface conditions are used to ensure continuities of the mass, momentum, and energy across the interface. Then, with the consideration of the interface radius of the curvature, the characteristic equation for the LRW is established and solved numerically by Muller's method. One important outcome is that there is weaker directional dependence for the velocity of the LRWs on the radius of curvature in comparison with the Rayleigh waves at an air-solid interface. However, the numerical results show a strong directional dependence for the attenuation due to the LRW leakage on the complex curvatures. Moreover, a quantitative relation between the curvature and attenuation caused by the leakage for different materials is shown. The results are significant especially with respect to relevant future applications of ultrasonic testing.

Dynamic Vibration Extinguished on a Viscously Elastic Base

The aim of the work is to develop algorithms and a set of programs for studying the dynamic characteristics of viscoelastic thin plates on a deformable base on which it is installed with several dynamic dampers. The theory of thin plates is used to obtain the equation of motion for the plate. The relationship between the efforts and the stirred plate obeys in the hereditary Boltzmann Voltaire integral. With this, a system of integro-differential equations is obtained which is solved by the method of complex amplitudes. As a result, a transcendental algebraic equation was obtained to determine the resonance frequencies, which is solved numerically by the Muller method. To determine the displacement of the point of the plate with periodic oscillations of the base of the plate, a linear inhomogeneous algebraic equation was obtained, which is solved by the Gauss method. The amplitude - frequency response of the midpoint of the plate is constructed with and without regard to the viscosity of the deformed element. The dependence of the stiffness of a deformed element on the frequency of external action is obtained to ensure optimal damping of vibrational vibrations of the plate.

Propagation of Natural Waves on a Multilayer Viscoelastic Cylindrical Body Containing the Surface of a Weakened Mechanical Contact

In this work, the study of the problems associated with the propagation of natural waves in multilayer viscoelastic cylindrical bodies with a weakened mechanical contact is discussed. A detailed analysis of well-known works devoted to this problem is given. A mathematical formulation, a technique, and an algorithm for studying the damping properties of natural waves in multilayered cylindrical mechanical systems with a weakened mechanical contact are developed. The solution of the considered problem was obtained by the method of separating the variables based on the theory of potential functions (special functions).The complex roots (phase velocities) of the dispersion transcendental equation for given wavenumbers are determined numerically by the Muller method. The phase and group velocities of a structurally heterogeneous mechanical system at various geometric and physical-mechanical parameters for the elements of the mechanical system are investigated. It was established that the real parts of the wave velocity will increase by only a few percent, and the imaginary parts for structurally heterogeneous mechanical systems radically change; the phase velocities (real parts of the complex velocity) of natural waves with an increasing wave numbers around the cylinder circumference of structurally heterogeneous mechanical systems first decrease and then begin to increase. A mechanical effect was discovered for structurally heterogeneous mechanical systems, which provides damping for the waves of the mechanical system as a whole.