In order to consider the effect of anisotropy of soil around the pile on the lateral vibration of pile groups, the soil around the pile is regarded as a transversely isotropic medium, and a lateral dynamic interaction model of pile-pile in transversely isotropic soil is established. According to Novak’s plane assumption and wave propagation theory, the lateral vibration of transversely isotropic soil layer is solved by introducing potential function and using mathematical and physical means, and the attenuation function of lateral displacement of free field is given. The Dobry and Dazetas simplified solution of attenuation function is different from that of solution of plane model. The pile-pile horizontal dynamic interaction factor in transversely isotropic soil is obtained by using the initial parameter method and Krylov function. The horizontal dynamic impedance of pile groups is obtained by using the pile-pile superposition principle. The change rule of the lateral displacement attenuation function of transversely isotropic soil with frequency is related to the direction and frequency. The ratio $G_{hv}$ of the shear modulus in the lateral plane to the shear modulus in the vertical plane and the pile spacing $S/d$ have a great impact on the lateral vibration of pile groups, and when the pile spacing is large, the curves of attenuation function varying with frequency fluctuate greatly. The ratio of elastic modulus of pile to vertical plane shear modulus of soil $E_p/G_v$ has an effect on the lateral stiffness of pile groups, which is related to frequency, while the effect on dynamic damping is not affected by frequency. The difference of mechanical properties on different surfaces of soil around the pile has a great influence on the lateral vibration of pile groups in transversely isotropic soil, and the influence of the anisotropy on the attenuation function of the lateral displacement and the dynamic impedance cannot be ignored.

A numerical investigation is carried out to analyze the impacts of internal heat source size, solid concentration of nanoparticles, magnetic field, and Richardson number on flow characteristics in an oppositely directed lid-driven wavy-shaped enclosure. The left and right vertical walls of the enclosure are cooled isothermally and moving with fixed velocity in upward and downward directions, respectively. The bottom wall is wavy shaped and isothermally cooled as the vertical walls while the top wall is kept adiabatic. A rectangular heater is placed horizontally in the center of the cavity. The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. The study is executed by analyzing different ranges of geometrical and physical parameters, namely, internal heat source length $\left(0.2\le \text{CH}\le 0.6\right)$ , solid concentration of nanoparticles $\left(0\le \phi \le 0.09\right)$ , Hartmann’s number $\left(0\le \text{Ha}\le 70\right)$ , and Richardson’s number $\left(0.1\le \text{Ri}\le 10\right)$ . The results indicate that the overall heat transfer rate declines with the increasing length of internal heat source. The presence and rising values of solid concentration of nanoparticles cause the augmentation of heat transfer whereas the magnetic field has a negative influence and the Richardson number has a positive influence on heat transfer.

In this paper, we utilized a hybrid method for the unsteady flow of the non-Newtonian third-grade fluid that combines the finite difference with the asymptotic interpolation method. This hybrid method is used to satisfy the semiunbound domain condition of the fluid flow’s length approaching infinity. The primary issue with this research is how much of the hybrid approach’s error may be accepted to guarantee that the method is significant. This paper discussed theoretical error analysis for numerical solutions, including the range and norm of error. The perturbation method’s concept is used to assess the hybrid method’s error. It is discovered that the hybrid approach’s relative error norm is lower than that of the finite difference method. In terms of the error standard, the hybrid approach is more consistent. Error analysis is performed to check for the accuracy as well as the platform for variable mesh size finite difference method in the future research.

The objective of this paper is to study the antidamage ability of beam column joints in complex steel structures under external forces and to improve the safety of such structures. In this study, a three-dimensional model of complex steel structure based on BIM technology is proposed by analyzing and calculating the ultimate strength of complex steel structure for mine protection. The vibration control algorithm of complex steel structure for mine protection is designed, and the boundary elastic constraint conditions are determined. According to the constraint conditions, the vibration characteristics of complex steel structures for mining are analyzed. The experimental results show that the maximum displacement of the design model is reduced by half compared with that before optimization, which can meet the design requirements.

In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease-free and endemic equilibrium points under certain conditions. The basic reproduction number, $R_0$ , is derived via the next-generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease-free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID-19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID-19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time-dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45.

The objective of this work is to investigate the influences of thermal radiation, heat generation, and buoyancy force on the time-dependent boundary layer (BL) flow across a vertical permeable plate. The fluid is unsteady, incompressible, viscous, and electrically insulating. The heat transfer mechanism happens due to free convection. The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. The impressions of thermal radiation and buoyancy forces are exposed in the energy and momentum equation, respectively. For numerical model, a set of nonlinear dimensionless partial differential equations can be solved using an explicit finite difference approach. The stability and convergence analyses are also established to complete the formulation of the model. The thermophysical effects of entering physical parameters on the flow, thermal, and material fields are analyzed. The variations in local and average skin friction, material, and heat transfer rates are also discussed for the physical interest. The analysis of the obtained findings is shown graphically, and relevant parameters pointedly prejudice the flow field. Studio Developer FORTRAN 6.2 and Tecplot 10.0 are applied to simulate the schematic model equations and graphical presentation numerically. The intensifying values of the magnetic field are affected decreasingly in the flow field. The temperature profiles decrease within the BL to increase the value of radiation parameters. The present study is on the consequences for petroleum engineering, agriculture engineering, extraction, purification processes, nuclear power plants, gas turbines, etc. To see the rationality of the present research, we compare these results and the results available in the literature with outstanding compatibility.

With the widespread use of embedded systems, chaos is a nonlinear system with certainty and complexity. It is an important topic in the field of information security at present, and it is an effective way to apply to embedded systems. It has great practical value in theory and in practice. This research mainly focuses on the encryption technology of SQLite embedded database and proposes an improved sparrow algorithm (Logistic Chaos Sparrow Search Algorithm, LCSSA) based on Logistic Chaos Map. It shows that the security level of SQLite in web development is higher than that of conventional Access. The population is initialized by the logistic chaotic mapping method, which improves the quality of the initial solution, increases the diversity of the population, and reduces the risk of premature maturity of the algorithm. The initial value $y_0$ determines the encryption method of the nonlinear function. Taking the integer variable (int) as an example, the value range is -231~231. It can be seen that the key space is sufficient to prevent various conventional attacks. When the key is the wrong key, decryption will not yield any data. It can be found that encryption and decryption are very sensitive to the key, which is also determined by the sensitivity of chaotic encryption system to the initial value. The benchmark function compares the performance of the improved algorithm with the algorithm before the improvement and compares it with the SSA. The LCSSA has better convergence performance, higher accuracy, and better stability.

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcation by using normal form theory and center manifold theorem are identified. Additionally, using numerical simulations and a hypothetical dataset, various dynamic characteristics are discovered, including stability switches, chaos, and Hopf bifurcation scenarios.

Identity information security is faced with various challenges, and the traditional identification technology cannot meet the needs of public security. Therefore, it is necessary to further explore and study new identification technologies. In order to solve the complex image preprocessing problems, difficult feature extraction by artificial design algorithm, and low accuracy of lip print recognition, a method based on the convolutional neural network is proposed, by building a convolutional neural network called LPRNet (Lip Print Recognition Network). The obtained lip print image is inputted into the training recognition model of the network to simplify the lip print image preprocessing. By extracting feature information and sampling operation, the model training parameters are reduced, which overcomes the difficulty of designing a complex algorithm to extract features. By analyzing and comparing the experimental results, a higher recognition rate is obtained, and the validity of the method is verified.

Crime is one among the most challenging problems in most developing countries in which unemployment is among the causes. Not all kind of crimes can be eradicated indeed; this paper is intended to contribute on eradication of unemployment-related crimes in the developing countries by proposing a deterministic mathematical model of unemployment-crime dynamics including vocational training and employment as control measures for crime. The study adopts the epidemiological model concepts on model formulation and model analysis while considering unemployment as main driver of crime. The basic properties of the model are analyzed, and well-posed of the model is established by using the Lipschitz condition. The next-generation matrix is used to obtain the criminal reproduction number which help to derive the conditions for local and global stability of the model. Moreover, the existence of backward and forward bifurcation when the crime reproduction number is equal to one was analyzed by center manifold theory. Simulations of the model are carried out to validate the theoretical part of the model and demonstrate vocational training, and employment strategies are more effective in combating crime when applied simultaneously. The findings suggest that unemployment problem should be addressed in order to reduce the number of unemployed individuals in joining the criminal activities.