Displacement Law Research Articles

Infrared Imaging Analysis as Non-Destructive Maintenance of Food Processing Equipment

The use of infrared imaging is a recently developed non-destructive tool to assess the safety, quality and efficiency of the food industry. This article explores the application areas and benefits of using infrared imaging in the maintenance of machinery used in the food industry. Applications covered include food quality control, packaging inspection, temperature monitoring and control, hygiene and sanitation control, foreign object detection, energy saving through optimization, baking, as well as cooking process monitoring and research. By using infrared cameras to their full potential, it is possible to reveal defects, check the level of cleanliness, optimize the maintenance of machines, and examine the thermal attributes of food. This article also provides an in-depth analysis of the historical development of infrared imaging technology. We also explore the basic ideas behind infrared image analysis. This includes the Stefan-Boltzmann Law, Planck's Law, and Wien's displacement law. Infrared image analysis has many advantages and some disadvantages. Despite these drawbacks, infrared imaging analysis has continued benefits. It saves costs, ensures equipment longevity and increases productivity. This makes it very important for the safety of food industry machinery.

Exploring the mechanism of infrared emissivity control in YSZ-based ceramics doped with Yb2O3

Due to its exceptional thermal stability and high conductivity, Yttrium stabilized zirconia (YSZ) has become an essential material in the field of infrared camouflage. Although YSZ exhibits relatively low emissivity within the 3–5 μm wavelength range, the increasing operating temperatures of aircraft necessitate further reduction in infrared emissivity within this specific band, in accordance with the Wien displacement law. This study focuses on the preparation of ceramic samples of YSZ doped with varying concentrations of Yb2O3 through a high-temperature solid-state reaction. It aims to investigate the influence of different doping concentrations on the microstructure, crystal structure, and infrared radiation characteristics of YSZ ceramic blocks. The experimental results demonstrated that the addition of Yb2O3 induces changes in the grain size and phase content of YSZ. Notably, as the amount of Yb2O3 doping increases, the infrared emissivity of YSZ samples in the 3–5 μm wavelength range exhibits a pattern of initial decrease followed by an increase. Remarkably, at a doping amount of 3 % mol, YSZ ceramics demonstrated the lowest emissivity, with the average emissivity of the 3–5 μm wavelength range decreasing from 0.41 to 0.38.

Nonlinear wave propagation in large extra spatial dimensions and the blackbody thermal laws

Abstract Nonlinear wave propagation in large extra spatial dimensions (on and above d = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant F ( = − ( 1 / 4 ) F μ ν F μ ν ) . In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan–Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien’s displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well.

Simultaneous thermal camouflage and radiative cooling for ultrahigh-temperature objects using inversely designed hierarchical metamaterial

Abstract Sophisticated infrared detection technology, operating through atmospheric transmission windows (usually between 3 and 5 μm and 8–13 μm), can detect an object by capturing its emitted thermal radiation, posing a threat to the survival of targeted objects. As per Wien’s displacement law, the shift of peak wavelength towards shorter wavelengths as blackbody temperature rises, underscores the significance of the 3–5 μm range for ultra-high temperature objects (e.g., at 400 °C), emphasizing the crucial need to control this radiation for the objects’ viability. Additionally, effective heat management is essential for ensuring the consistent operation of these ultrahot entities. In this study, based on a database with high-temperature resist materials, we introduced a material-informatics-based framework aimed at achieving the inverse design of simultaneous thermal camouflage (low emittance in the 3–5 μm range) and radiative cooling (high emittance in the non-atmospheric window 5–8 μm range) tailored for ultrahigh-temperature objects. Utilizing the transfer matrix method to calculate spectral properties and employing the particle swarm optimization algorithm, two optimized multilayer structures with desired spectral characteristics are obtained. The resulted structures demonstrate effective infrared camouflage at temperatures up to 250 °C and 500 °C, achieving reductions of 86.7 % and 63.7 % in the infrared signal, respectively. At equivalent heating power densities applied to the structure and aluminum, structure 1 demonstrates a temperature reduction of 29.4 °C at 0.75 W/cm2, while structure 2 attains a temperature reduction of 57.5 °C at 1.50 W/cm2 compared to aluminum, showcasing enhanced radiative cooling effects. This approach paves the way for attenuating infrared signals from ultrahigh-temperature objects and effectively managing their thermal conditions.

Incandescent Lamp from Black Body Perspective

The incandescent lamp from black body perspective was investigated using commercial lamps of various watts. The major component of the incandescent lamp is the tungsten filament. The resistance of the tungsten filament was measured using a digital multimeter at an initial laboratory temperature. Light produced from lamp was separated into visible colours by an equilateral triangular glass prism. Deduced resistances were used to obtain equivalent temperatures by power-law parameterization. The Wien’s displacement law was used to estimate Peak wavelengths at different temperatures. The diameter of the tungsten was measured after dissecting the lamp, and this was used to determine its cross-sectional area. Both Wien’s displacement law and Stefan-Boltzmann expressions were applied in determining the filament’s spectral emissive power (SEP) in comparison with that of the visible spectrum. Planck’s graph of intensity using peak wavelength of tungsten filament as reference was juxtaposed with the intensity of visible spectrum using OriginPro 2016 SR0 b9.3.226. The maximum temperature attained was 2852.87 K with (SEP) of 1478955.24 Wm-2 for the 200W lamp. For the 100W lamp, the (SEP) obtained was 749347.9078 Wm-2 at 2489.14 K. Both temperatures, and even as low as 1250 K, were in agreement with Wien’s displacement law. The percentage estimation of visible spectrum in the radiation was about fourteen percent (14 %) while the rest was infra red radiation. This low visible light produced may be as a result of the non-ideal black body nature of the tungsten filament; and so, the incandescent lamp may be considered a quasi-black body.

Displacement and pressure of surrounding rock during shield tunnelling and supporting in low water content loess

Using a self-developed micro shield machine, a laboratory-scale experimental scheme for shield tunnelling and supporting was designed, and the soil displacement law and earth pressure on the segments during tunnel construction were studied. Based on a nonlinear elastic constitutive model describing the characteristics of loess, the UMAT subroutine was redeveloped and verified by conventional triaxial tests. It was then applied to the numerical simulation of shield tunnelling and supporting. The following are the findings: 1) The disturbance modes of surrounding rock directly above the shield tunnel under different boundaries are similar. The main disturbances occur approximately 4 m above the shield tunnel, extending to a distance of one segment outer diameter on either side of the tunnel's central axis. 2) The pressures on the top and bottom of the segments can be divided into rapid increase, slow increase, and stable fluctuation. These stages correspond to the processes of the segments getting out of the shield shell and the soil collapsing. 3) The largest surrounding rock pressure is at the vault, followed by that at the arch bottom, and the smallest is at both sides of the arch waist, which is consistent with the law obtained based on laboratory-scale model tests. The surrounding rock pressure values of the vault in the numerical simulation are consistent with the laboratory-scale model test results. These verify the reliability of the laboratory-scale model test and the UMAT subroutine based on the nonlinear elastic constitutive model of loess in simulating the shield tunnel construction in loess strata.

Numerical Analysis of the Dynamic Response of Concrete Bridge Piers under the Impact of Rock Debris Flow

The impact and damage caused by debris flow on concrete bridges have become a typical disaster scenario. However, the impact disaster mechanism of debris flow on bridge structures remains unclear. This study focused on investigating the impact mechanism of debris avalanches on concrete bridge piers. By employing the discrete element numerical simulation method to examine the effect of debris on concrete bridge piers, the analysis explored the influence of three significant factors: the pier’s section shape, the impact distance, and the slope angle of the sliding chute. The discussions included the accumulation pattern of rock debris, the impact force on the pier, and the shear force and bending moment at the pier’s bottom, as well as the displacement and velocity response laws at the pier’s top. The results demonstrate that rectangularly shaped piers have a high efficiency in obstructing debris, leading to higher impact forces and internal forces on piers. Arched-shaped piers exhibit a short-duration, high-peak instantaneous impact from debris. Increasing the impact distance of the piers can significantly reduce the impact force of debris. The accumulation height of debris, pier impact force, and the pier’s bottom internal forces decrease and then increase with the increase in slope angles, with a 45° slope angle being the critical point for the transition of debris impact on piers. The results can provide references for the disaster prevention design of concrete bridge structures in hazardous mountainous areas.

Study on two-phase displacement law considering mass transfer and diffusion

The influence of channeling on viscous fingering instability of CO2 miscible displacement is studied in the paper. Due to the viscous fingering not easily observed in porous media, channeling is used to simplify the viscous fingering instability. We adopted nonlinear simulation to investigate the development of viscous fingering instability during the displacement of Newtonian fluids in a channel by miscible fluids, and the influence of different Pe and different viscosity ratio R was studied. Under homogeneous conditions, when R is the same, the larger the Pe is, the more obvious the convection in the process of CO2 displacement is, the earlier the viscous fingering occurs, and the shorter the time for the finger to break through to the right boundary is. When Pe is the same, the larger the R is, the more unstable the contact area of miscible displacement becomes. More finger structures appear, and more complex fingering phenomena occur. The larger the R is, the earlier the fingering phenomenon appears, and the earlier it breaks through to the right boundary. In addition, we studied the change in Relative Mixing Length (RML) during the diffusion process quantitatively. Finally, our investigation delved into the impact of heterogeneity on viscous fingering. We observed that under significant heterogeneity, viscous fingering tends to manifest preferentially in the direction of increasing permeability.

Study on overburden failure characteristics and displacement rule under the influence of deep faults

Deep faults significantly impact the structural stabilities and deformation behaviors of their overburden rocks, which are key factors in underground engineering and geological hazard research. Considering the problem of deep-fault-overburdened breaking during mining of super-thick coal seams and taking the Yaoqiao Coal Mine as the research object, the mining fracture evolution characteristics and overburden displacement law of the non-structured and fault-bearing overburden corresponding to fully mechanized caving mining are compared and analyzed using numerical simulations and physical similarity simulations. The results of this study show the following: 1) The fracture height of the overlying rock presents a specific change law with advancement of the working face; the initial rapid increase to a maximum height of 74 m is achieved when the working face advances to 90 m; with the development of the plastic zone indicating past yield, the fracture height decreases to 54 m and becomes stable, and the final caving angle of the fracture stabilizes at 70°. 2) In coal mining under normal fault conditions, when the working face advances from the upper to lower walls, the roof forms a masonry beam structure that slows down fault activation and crack development. When moving away from the fault, the overburden movements and water-conducting cracks are fewer, and the crack height is lower than that without faults. When approaching the fault, the influence of the faults in the fracture zone increases, and the height of fracture development reaches the maximum value after crossing the fault, highlighting the significant influence of the fault on fracture development. 3) Through a similarity simulation test, it is shown that the overburden caving zone is further compacted by the overburden rock and that the roof collapses in a large range, resulting in rapid upward development of the overburden rock cracks and separation of the central overburden rock cracks that are gradually compacted and closed. These findings are expected to have important theoretical and practical significance for deep underground engineering design, geological disaster prevention, and fault activity monitoring.

Adiabatic invariance and its application to Wien's complete displacement law of blackbody radiation

We derive the “complete” or “strong” version of Wien's displacement law from two adiabatic invariants: one of a thermodynamic system composed of a finite-sized segment of frequencies taken from the spectrum of blackbody radiation and one of the individual electromagnetic waves that compose this system. By exploiting the algebra of these invariants, we shift the calculational burden of deriving Wien's displacement law toward the methods of classical thermodynamics. These methods also produce a class of displacement laws that constrain both the particles of a classical ideal gas and the acoustic waves of the Debye model of a solid.

Experimental Study on Stability Analysis of Shallow-Buried Metro Station Hard Rock Excavation under Blasting Vibration Effect

Abstract By considering a certain metro station of Qingdao Metro Line 4 as the research object, a three-dimensional geotechnical testing model has been developed to analyze the stress and deformation characteristics of the surrounding rocks under blasting vibration effect. The simulation of the surrounding rock blasting process is achieved through an electric spark source. We conducted simulation tests on the excavation stability of shallow-buried hard rock metro stations with and without considering blasting damage effects, respectively. The stress, displacement, and primary support stress changing laws of the surrounding rock under different overburden thicknesses using the arch cover method and the primary support arch cover method have been revealed. Finally, we analyzed the applicability of the primary support arch cover method in terms of vault settlement, clearance convergence, and floor heave. Results show that the surrounding rock of the arch has roughly gone through three deformation stages, namely a slow deformation stage, rapid deformation stage, and stable deformation stage. Whether it is blasting excavation or non-blasting excavation, the settlement of the arch is within a safe and controllable range. Because of the refinement of the excavation process by the primary support arch cover method, the stress release is relatively stable throughout the entire excavation process, but the significant impact of blasting vibration on the surrounding rock cannot be ignored. The excavating of the left and right guide holes is the key process for the displacement and stress variation. The deformation and stress generated by the arch cover method have a small difference compared to the deformation and stress generated by the primary support arch cover method, indicating that the latter excavation method can be used under current engineering geological conditions. No large-area collapse and instability occurred in the experimental process, which provides a theoretical basis for similar projects.

Stability Analysis of Slopes Supported by Anti-slip Piles under Different Working Conditions

In the reinforcement of slope management measures, the arrangement of anti-slip piles is often used to keep the slope stable, and anti-slip piles, as a typical landslide prevention and control structure, occupy a more important position in landslide management. Relying on a landslide in Gansu Province, this paper carries out numerical simulation research on landslide reinforced by anti-slip piles to study the change rule of the stability coefficient of the landslide under natural, rainfall and earthquake conditions as well as the displacement law under earthquake conditions, and then evaluates the reinforcing effect of anti-slip piles in the management of landslides. The results of the study show that, before the landslide was reinforced by anti-slip piles, the landslide mass was in a stable state and a basically stable state under natural conditions and rainfall conditions, respectively, and the probability of failure was small. Under the earthquake condition, the landslide is in an unstable state and is prone to localized failure, and the displacement of the landslide mass in the X direction is larger; The stability coefficients of the landslide mass under each condition were greatly improved after the stabilization of the landslide by anti-slip piles and the X-direction was limited under the earthquake condition, and the landslide was in a stable state. The effect of anti-slip pile reinforcement is good, and it can provide reference for future anti-slip pile reinforcement slope projects.

Study on displacement and imbibition law of tight sandstone reservoir

Due to the rapid increase of the world's energy demand, people gradually put the focus of oil and gas development on unconventional. Tight reservoir as an important part of unconventional, how to improve the recovery rate of tight reservoir has become the focus of the times. In this paper, the relationship between oil saturation and recovery rate of tight reservoir is explained by displacement and imbibition experiments on cores with different oil saturation, and the mechanism is explained by nuclear magnetic resonance, which provides direction for improving the recovery rate of tight reservoir.

Some Interesting Facts About Planck’s Law of Blackbody Radiation

Introductory textbooks of Modern and Thermal Physics discuss the Planck radiation law as a backbone of the blackbody radiation spectrum. This law is used to explain the intensity of blackbody radiation as a function of either frequency or wavelength at a given temperature. In the introductory coursework, the Planck’s formula is also used to study other blackbody radiation laws such as Stefans–Boltzmann law, Wien’s Displacement law, Rayleigh–Jeans Law and Wien’s Distribution law. In this work, we highlight some interesting facts related to the total energy density, photon number density and average energy of photon of blackbody radiation. The main objective of this work is to focus on the lesser known features associated with physics of blackbody radiation. We believe that these simple analytic calculations may give very useful and interesting information about the Planck radiation law to the undergraduate students.

Study on Methane Displacement Law of Coal with Different Metamorphic Degrees by N2 Injection

Study on Methane Displacement Law of Coal with Different Metamorphic Degrees by N2 Injection

Theoretical analysis of stratum horizontal displacements caused by small radius curve shield tunneling

For small radius curve shield tunneling, over excavation is required on the inner side of the curve to corner the shield machine. Currently, there is no corresponding analytical solution for horizontal displacements. In this paper, using the image method and Mindlin solution and considering four factors: additional thrust on the excavation surface, frictional resistance of the shield shell, ground loss, and grouting pressure at the shield tail, a formula for calculating stratum horizontal displacements caused by small radius curve shield tunneling is derived. Based on the 220 kV Rhinoceros Station cable shield tunnel project in Guangzhou, the stratum horizontal displacement law and influencing factors are analyzed. Through comparison and verification with on-site measured data, the results indicate that the theoretical formula derived is reasonable and reliable, providing a new approach for predicting the stratum horizontal displacements induced by curve shield tunneling. The law of stratum horizontal deformation exhibits that the horizontal displacement caused by the over excavation side of the curve moves toward the tunnel side. The outer side of the curve shifts away from the tunnel. The peak appears near the axis of the shield tunnel. The ground loss has the most significant influence on stratum horizontal displacements. Furthermore, on the same tunnel cross-section, the closer the soil is to the tunnel, the greater the horizontal displacement of the soil, and vice versa. The change in shield shell length profoundly affects horizontal displacements. The friction difference coefficient has a significant impact on the stratum horizontal displacement outside the curve.

Mechanical Response Law and Parameter Influence Analysis of Karst Tunnel Dynamic Excavation

To ensure the stability of the tunnel structure, this paper simulates the excavation process of shield tunneling in karst areas, and monitors the top of the arch, the bottom of the arch and the waist of the arch within the influence of the cave. It obtains the displacement and stress change laws under the influence of the upper cave and the lower cave. Finally, the main factors causing karst collapse in tunnels are explored through orthogonal tests. The results indicate that the displacement of the surrounding rock within the influence of the cave decreases and the stress increases. When the cavity and the tunnel reach the safety limit distance, the effect of the lower cavity on the stress around the tunnel is more obvious than that of the upper cavity. The results of the orthogonal test show that when the cavity is above the tunnel, the tunnel burial depth has the greatest influence on the stability of the surrounding rock; when the cavity is below the tunnel, the cavity height has the greatest influence on the stability of the surrounding rock.

Application Design of Newton-Rapshon method in Proving Maximum Wavelength on Wien’s Displacement Law

The Calculation of the maximum wavelength (?m) of radiation emitted by a black body can be determined from the Wien displacement law, which states the ratio between the Wien constant and the absolute temperature (T). Wien's displacement law can be derived analytically from the Energy Density equation (U?) in Plank's law. The solution for U? is obtained by calculating the first derivative of the function with respect to ? or dU?/d?, and then proceeding with finding a solution to the equation for the derivative. The solution of dU?/d? is the value of ? that makes dU?/d? equal to zero. The resulting wavelength is the maximum wavelength ?m, which is the wavelength value that makes the value in the equation U? the maximum value. The final result of this calculation is the Wien’s displacement law, namely the multiplication of ?m with T equals the Wien constant. So basically, the derivation of Wien's displacement law is to find the maximum value of the function f(x). The maximum value of the function f(x) can be done numerically. Solving numerically can be done with the Modified Newton-Rapshon method. The modified Newton-Rapshon method is usually implemented in the form of computer program code. In this research, the results of the calculation of the maximum wavelength ?m analytically are very close to the results of numerical calculations (modified NR). This can be seen from the results of linear regression with gradient values (m), regression constants (c) and coefficient of determination (R2) close to the ideal values of 1, 0 and 1, respectively.

Similar simulation of overburden movement characteristics under paste filling mining conditions

The method of filling mining can solve the problem of surface subsidence caused by coal mining. Among them, it is crucial to study the mechanism of filler strength improvement timeliness and filler mining to control rock movement for filler mining. In this paper, by combining theoretical analysis and similar simulation experiments, compressive strength is used as the research parameter to conduct proportioning test research on paste filling similar materials such as coal gangue, fly ash, and cement. The results prove that the strengths of the test ratios can meet the strength design criteria and lay the foundation for the requirements of similar simulation experiments. In order to study the characteristics of overburden failure, stress and displacement in the process of filling mining, the key technical parameters of overburden movement are determined. Similar simulation experiments were conducted to study the movement and deformation of overburden rock and the displacement and stress distribution law of overburden rock in the coal mine under different filling rates and filling steps conditions. The results show that the filling rate and filling step are the keys to preventing the overlying rock from rupture and collapse, and the larger the filling rate is, the smaller the stress and displacement of the overburden; the larger the filling step is, the larger the displacement and stress change of the overburden, and vice versa. In addition, the displacement curve along the strike is basically an "arch" type distribution, and the stress variation trend is "large-small-large" with a "Z" type distribution. The research results are of great significance to guide the practice of filling mining and can provide the theoretical basis for its further promotion.

The Teaching Application of the Backward Design Method in Chinese National Undergraduate Engineering Training Integration Ability Competition: Take the Double 8 Carbon-Free Car as an Example

National Undergraduate Engineering Training Integration Ability Competition is essential in Chinese engineering colleges. Among these items, the carbon-free car competition is popular among college students because of its flexible track, challenging design tasks, and fair judging criteria. In this study, to design a reasonable carbon-free car structure according to the track given by the competition, a reverse analysis method was proposed for the double 8-shaped carbon-free car trajectory based on the space cam mechanism. First, the carbon-free car’s structure was designed, and its stress state was analyzed, with the results indicating that the driving force should be reduced as much as possible under the premise of satisfying the starting requirements to increase the travel distance of the carbon-free car with no slipping. Then, the function between the car track and the front wheel swing angle was established, and the displacement law of the push rod of the cam mechanism was calculated through the swing angle of the front wheel. Finally, the cam profile was got based on the operating law of the push rod. Research has shown that compared with the traditional forward design, this method was more accurate with strong feasibility and operability, which provided good technical support for designing the subsequent carbon-free car competition.