Comparison of Calculation Methods of Elastic Bonding: Limits of the Gamma Method Using an Example of a Wood–Concrete Composite Floor with Single Loads

Various methods are available for the calculation of timber–concrete composite floors. The gamma method, which is important in construction practice, as well as the differential equation method, are based on the simplified assumption of a continuous bond between wood and concrete. This makes it possible to analytically calculate the internally statically indeterminate partial section sizes and deformation sizes, analogous to the force size method. In this paper, two typical load situations of concentrated loads (central and off-centre) were analytically and numerically evaluated and compared using the above-mentioned methods (gamma and differential equation), with a discrete method for the case of a timber beam reinforced with a concrete slab using screws as fasteners. The calculation results show significant deviations, which speak for the application of discrete methods in certain load situations and thus limit the usability of the gamma method under certain conditions. For the problem of deflection determination, which is not dealt with in the literature for the discrete method, a numerical method is described in the present work, which was first developed and presented by the first author.

Electromagnetic Wave Equation Approximation using FDTD method on Conductivity Material

FDTD is a method that is applied in the simulation of electromagnetic waves. This study aims to simulate the propagation of electromagnetic waves on a material with conductivity and permittivity on the plate. The approximate form of Maxwell’s equations can be used to describe discrete electromagnetic waves. Signal analysis in the form of electromagnetic waves using position domains for magnetic field H and electric field E. By taking into consideration boundary conditions, stability, and boundary conditions, the proposed research employs the basic concept of differential equation method. The simulation results show that materials with high conductivity will cause the waves to decay. Under certain conditions, the relationship between the shape of the field to changes in conductivity and permittivity of the material is needed in the analysis process.

Partial Differential Equations-Based Iterative Denoising Algorithm for Movie Images

Film video noise can usually be defined as the error information visible on the video image, caused by the digital signal system. This distortion is inevitably present in the video obtained by various camera equipment. Noise reduction techniques are important preprocessing processes in many video processing applications, and its main goal is to reduce the noise contained in a video image while preserving as much of its edge and texture information as possible. In this paper, we describe in detail the principles of the space-time noise reduction filter, propose a 3D-filter algorithm for Gaussian noise, an improved 3D-filter algorithm based on the 3D-BDP (bloom-deep-split) filter for mixed noise, and a filter algorithm for luminance and color noise in low-brightness scenes. By dissecting the partial differential equation (PDE) denoising process, we establish a new iterative denoising algorithm. The partial differential equation method can be considered as the iterative denoising of the filter, and the first stage of the new algorithm uses wavelet-domain adaptive Wiener filter as the filtering base and achieves good results by adjusting the parameters. The proposed model in this paper is compared with the existing denoising model, and the analysis results show that the model proposed in this section can effectively remove multiplicative noise. The experimental report shows that the parameters set by the algorithm have some stability and can achieve good processing results for multiple images, which is an advantage over the partial differential equation method for denoising. The second stage of the algorithm uses the appropriate partial differential equation method to remove the pseudo-Gibbs in the first stage, which further improves the performance of the algorithm. After the image containing Gaussian noise is processed by the new algorithm, the pseudo-Gibbs effect, which often occurs in wavelet denoising, is eliminated, and the step effect, which occurs in partial differential equation denoising, is avoided; the details are better preserved, and the peak signal-to-noise ratio is improved, and a large number of experiments show that it is an effective denoising method.

Automatic Recognition Method of Letter Images in English Self-Learning Based on Partial Differential Equation Method

According to the current situation of knowledge popularization, students simply rely on the knowledge learned in the classroom that is far from adapting to the development of modern society; so, every student needs to have the consciousness and ability of independent learning. The research of the English self-help learning system based on partial differential equation method comes into being with information network technology as the foundation for survival and development. The existing partial differential equation recognition models based on average curvature motion are all edge-based and need to use the external force defined by the image gradient to attract the zero level set (evolution curve) to move to the target edge and finally stay on the target edge. Therefore, it is difficult to obtain ideal results when extracting fuzzy or discrete boundaries (perceptual boundaries), and it is very sensitive to the selection of initial contour and noise. To solve this problem, this paper proposes a new recognition model of partial differential equations based on mean curvature motion. This overcomes some defects of existing edge models because it is region-based and does not require image gradient as a condition to stop evolution. The proposed model can avoid manual initial curve selection and allow stopping conditions to be set in the algorithm. In addition, in the numerical solution of partial differential equations, the existing model uses upwind difference scheme, and the semi-implicit additive operator separation method is adopted in this paper. Some other layers are added, and some hyperparameters are adjusted when the convolutional neural networks of inception PDEs are constructed by stacking the structure of inception PDEs. In the contrast experiment with the prototype, the software and hardware environment are the same, and the input is exactly the same. For the handwritten English alphabet data set, the variant structure can obtain more than 90% of the training accuracy and verification accuracy, which is better than the experimental accuracy of the prototype. In addition, because the inception PDE structure contains fewer parameters than the prototype, it is more computationally efficient and takes less training time per batch than the prototype.

Extraordinary optical transmission through periodic Drude-like graphene sheets using FDTD algorithms and its unconditionally stable approximate Crank–Nicolson implementation

Based upon the approximate Crank–Nicolson (CN) finite-difference time-domain method implementation, the unconditionally stable algorithm is proposed to investigate the wave propagation and transmission through extremely thin graphene layers. More precisely, by incorporating the CN Douglas–Gunn algorithm, the piecewise linear recursive convolution method and the auxiliary differential equation method, the analytical model is proposed for Drude-like graphene model. To obtain the solution of the governing equations, the perfectly matched layer and the periodic boundary condition are applied to the graphene structure with two dimensional nano-materials. Numerical examples are carried out for further investigation. During the simulation, the influences of the parameters such as the grating slit and its thickness on the wave transmission are investigated and discussed. The result shows that not only the graphene grating has high transmission performance but also the proposed methods have considerable performance and accuracy.

The evolution equation of non-linear waves and its exact solutions by subsidiary ordinary differential equation method

In this work, we investigate the dynamics of the equatorial Rossby waves by including the complete Coriolis force, external source and dissipation. The amplitude evolution of equatorial Rossby waves is described as an extended non-linear mKdV–Burgers equation from a potential vorticity equation and it is unlike the standard mKdV–Burgers equation. Built on the obtained model, the corresponding physical phenomena related to the non-linear Rossby waves are analyzed. Also, the subsidiary ordinary differential equation method is employed to solve the solitary solution of the mKdV equation. By analyzing the solution, we find that the horizontal component of Coriolis parameter works on the amplitude of the Rossby waves. Meanwhile, we use the Adomian decomposition method to obtain the approximate soliton solution of the model.