Explore the vast range of titles available.

In this paper, by means of a proper orthogonal decomposition (POD) we mainly reduce the order of the classical Crank–Nicolson finite difference (CCNFD) model for the fractional-order parabolic-type sine-Gordon equations (FOPTSGEs). Toward this end, we will first review the CCNFD model for FOPTSGEs and the theoretical results (such as existence, stabilization, and convergence) of the CCNFD solutions. Then we establish an optimized Crank–Nicolson finite difference extrapolating (OCNFDE) model, including very few unknowns but holding the fully second-order accuracy for FOPTSGEs via POD. Next, by a matrix analysis we will discuss the existence, stabilization, and convergence of the OCNFDE solutions. Finally, we will use a numerical example to validate the validity of theoretical conclusions. Moreover, we show that the OCNFDE model is very valid for settling FOPTSGEs.

The temperature distribution is one of the most vital parameters which should be fully considered in high geothermal tunnel design. For the purpose of studying the impact of temperature disturbance caused by construction on temperature distribution of surrounding rock and lining structure in a high geothermal tunnel, a new finite difference model for temperature prediction was proposed. Based on the abundant field test results, forecast analysis for the research of a high geothermal tunnel in this paper is made. The results indicate that the temperature of the surrounding rock near the tunnel sidewall decreases obviously in the first 14 days while that of the surrounding rock far away is stable after tunnel excavation, and the rock temperature showed three ways of change: undulate type (<2 m), decline type (2–5 m) and stable type (>5 m). There is a linear relationship between the initial rock temperature and the released heat of the surrounding rock. The radius of the heat-adjusting layer and the initial rock temperature presents a quadratic function relation. The lining concrete actually cures under the variable high-temperature environment and the real curing temperature decreases with time and becomes stable seven days later. The results would contribute to providing support for high geothermal tunnel research and design.

PurposeThe induction of geological disasters is predominantly influenced by the dynamic evolution of the stress and plastic zones of the multilayer rock formations surrounding deep-rock roadways, and the behaviours and mechanisms of high in situ stress are key scientific issues related to deep-resource exploitation. The stress environment of deep resources is more complex owing to the influence of several geological factors, such as tectonic movements and landforms. Therefore, in practical engineering, the in situ stress field is in a complex anisotropic three-dimensional state, which may change the deformation and failure law of the surrounding rock. The purpose of this study is to investigate the tunnelling-induced stress and plastic evolution causing instability of multilayered surrounding rock by varying three-dimensional in situ stresses.Design/methodology/approachBased on data from the Yangquan Coal Mine, China, a finite difference model was established, and the elastic-plastic constitutive model and element deletion technology designed in the study were analysed. Gradual tunnelling along the roof and floor of the coal seam was used in the model, which predicted the impact tendency, and compared the results with the impact tendency report to verify the validity of the model. The evolutions of the stress field and plastic zone of the coal roadway in different stress fields were studied by modifying the maximum horizontal in situ stress, minimum horizontal in situ stress and lateral pressure coefficient.FindingsThe results shown that the in situ stress influenced the stress distribution and plastic zone of the surrounding rock. With an increase in the minimum horizontal in situ stress, the vertical in situ stress release area of the roof surrounding rock slowly decreased; the area of vertical in situ stress concentration area of the deep surrounding rock on roadway sides decreased, increased and decreased by turn; the area of roof now-shear failure area first increased and then decreased. With an increase in the lateral pressure coefficient, the area of the horizontal in situ stress release area of the surrounding rock increased; the area of vertical in situ stress release area of the roof and floor surrounding rock first decreased and then increased; the area of deep stress concentration area of roadway sides decreased; and the plastic area of the surrounding rock and the area of now-shear failure first decreased and then increased.Originality/valueThe results obtained in this study are based on actual cases and reveal the evolution law of the disturbing stress and plastic zone of multilayer surrounding rock caused by three-dimensional in situ stress during the excavation of deep rock roadways, which can provide a practical reference for the extraction of deep resources.

The paper presents a new electrothermal microgripper with a large amplification ratio and a single photo mask. This microgripper is designed with the 40‐μm‐stroke, which is 3.33 times larger than displacement of the driving V‐shaped actuator. It is successfully fabricated by using SOI‐MEMS technology, with an additional platinum sputtering step to reduce equivalent resistance of V‐beams system as well as the power consumption. The experimental displacement has been tested and compared with nonlinear calculations and simulation results. At a driving voltage of 10 V, the microgripper achieved a displacement of 36 μm, compared to the calculated and simulated values of 45.3 and 40.9 µm, respectively.

Investigation of heavy metal transport in water bodies such as dam reservoirs due to the environmental hazards and the transformation complexities of heavy metals from dissolved phase to particulate phase and vice versa is of particular importance. The transport process of the dissolved heavy metals such as lead (Pb) in storage dam reservoirs is significantly influenced by the water flow, and ambient parameters such as temperature, total dissolved solids (TDS), dissolved oxygen (DO), and suspended solids (SS). Due to the lack of a suitable model to simulate the heavy metal transport in dam reservoirs, in this study, the hydrodynamics and water quality model, CE-QUAL-W2, was enhanced by developing 2D laterally averaged model for simulating the dissolved phase of Pb contaminant and applied to the Shahid Rajaei Dam reservoir, Sari, Iran. The developed model can describe the advection–dispersion and transformation processes and simulate the temporal and spatial distribution of dissolved phase of Pb concentrations. A new approach was introduced to calculate different reaction coefficients used in the transformation term of the advection–diffusion equation. Comparison of the simulation results of temperature, TDS, DO, SS, and dissolved phase of Pb with the measured values from the Shahid Rajaei Dam reservoir shows a mean percentage error (MPE) of 6.8, 4.7, 11.7, 19.7, and 7.27 respectively. The results of the present study showed that the temperature was the most effective parameter on the transformation of Pb in the Shahid Rajaei Dam reservoir due to large changes of temperature in depth as about 15 °C along with small changes in other ambient parameters in several months of the year. This phenomenon can be expected in many reservoirs that are stratified in a period of the year. However, the effect of other ambient parameters such as TDS, DO, and SS should not be neglected.

This study presents a 1D finite difference model that examines the influence of cloth fabrics on skin temperature during and after exercise, considering the complex nature of the human body and its susceptibility to infections and viruses. The aim is to design comfortable, high-quality fabrics that minimize potential issues caused by body temperature fluctuations. The model incorporates various physical, physiological, and thermal parameters of cloth to develop protective clothing suitable for exercise. Numerical results were compared to previous studies that analyzed skin temperature without clothing to validate the model’s accuracy. The findings indicate a minimal difference in skin temperature when wearing cotton and polyester cloth, with polyester fabric demonstrating superior characteristics such as stretchability, durability, and sweat resistance. The thermal information obtained from this model can be utilized to design appropriate clothing for diverse weather conditions, ultimately enhancing the performance and comfort of athletes, military personnel, and individuals engaged in physically demanding work. Additionally, the model can aid in developing thermal stress protocols for infection treatment and provide guidelines for physical activity to promote healthy living. This research contributes to the field of materials research by offering valuable insights into the design and development of protective clothing for exercise. By understanding the impact of cloth fabrics on skin temperature, advancements can be made in creating clothing that optimizes human comfort and performance.

Study of the saturated‐unsaturated flow in porous media is of interest in many branches of science and engineering. Among the various numerical simulation methods available, the finite difference method is advantageous because it offers simplicity of discretization. This method has been widely used for simulating saturated‐unsaturated flows. However, the simulation of geometrically complex flow domains requires the use of high‐resolution grids in conventional finite difference models because conventional finite difference discretization assumes an orthogonal coordinate system. This makes a finite difference model computationally less efficient than other numerical models that can treat nonorthogonal grids, such as the finite element model and finite volume model. To overcome this disadvantage, we use a coordinate transformation method and develop a multidimensional finite difference model for simulating saturated‐unsaturated flows; this model can treat nonorthogonal grids. The cross‐derivative terms derived by the coordinate transformation method are evaluated explicitly for ease of coding. Therefore, a 7 point stencil is used for implicit terms in the iterative calculation, as in the case of conventional finite difference models with an orthogonal grid. We assess the performance of the proposed model by carrying out test simulations. We then compare the simulation results with dense grid solutions in order to evaluate the numerical accuracy of the proposed model. To examine the performance of the proposed model, we draw a comparison between the simulation results obtained using the proposed model and the results obtained by using (1) a model in which all terms are considered fully implicitly, (2) a finite element model, and (3) a conventional finite difference model with a high‐resolution orthogonal grid.

The boundary-element method (BEM) is widely used for electrocardiogram (ECG) simulation. Its major disadvantage is its perceived inability to deal with the anisotropic electric conductivity of the myocardial interstitium, which led researchers to represent only intracellular anisotropy or neglect anisotropy altogether. We computed ECGs with a BEM model based on dipole sources that accounted for a “compound” anisotropy ratio. The ECGs were compared with those computed by a finite-difference model, in which intracellular and interstitial anisotropy could be represented without compromise. For a given set of conductivities, we always found a compound anisotropy value that led to acceptable differences between BEM and finite-difference results. In contrast, a fully isotropic model produced unacceptably large differences. A model that accounted only for intracellular anisotropy showed intermediate performance. We conclude that using a compound anisotropy ratio allows BEM-based ECG models to more accurately represent both anisotropies.

Departing from a general stochastic model for a moving boundary problem, we consider the density function of probability for the first passing time. It is well known that the distribution of this random variable satisfies a problem ruled by an advection–diffusion system for which very few solutions are known in exact form. The model considers also a deterministic source, and the coefficients of this equation are functions with sufficient regularity. A numerical scheme is designed to estimate the solutions of the initial-boundary-value problem. We prove rigorously that the numerical model is capable of preserving the main characteristics of the solutions of the stochastic model, that is, positivity, boundedness and monotonicity. The scheme has spatial symmetry, and it is theoretically analyzed for consistency, stability and convergence. Some numerical simulations are carried out in this work to assess the capability of the discrete model to preserve the main structural features of the solutions of the model. Moreover, a numerical study confirms the efficiency of the scheme, in agreement with the mathematical results obtained in this work.

With the development of electronic packaging technology, the time criterion and the space criterion of heat transfer have been becoming smaller and smaller, which results in the stronger Non-Fourier effect．Using the classical Fourier model to analyze the heat transfer of the substrate will inevitably make the result deviate from the actual conditions greatly. However, using the Non-Fourier model could closely describe the real situation. This paper regards the Fourier model and the Non-Fourier model separately, sets up their own mathematics-physics equations to the heat-transfer model of three-dimension multi-chip module(MCM) substrate，adopts finite difference method(FDM) to solve the corresponding equations，and get the temperature field of the three-dimensional substrate model. To test the accuracy of the results, meanwhile, the thermal analysis software ANSYS ICEPAK is used to calculate the same model. The results indicate that，compared with the classical Fourier model，the results of Non-Fourier model have great advantages：the temperature value is higher, the time is longer for temperature field to enter the stable state, changing of the temperature is faster and the phenomenon of thermal coupling is stronger too.