Quantitative Laws Research Articles

Algorithm for Evaluating the Effectiveness of Compositional Equilibrium of Graphical User Interfaces

Formulation of the problem: with the rapid development of information technology, numerous analogues of multidisciplinary programs are increasingly appearing on the software market. Despite the similarity of functions and identical sets of tools, these programs have different graphical user interfaces - program shells that provide the user with the opportunity to interact with the program using logic. In most cases, the overall assessment of users regarding the quality of programs depends on the effectiveness of interfaces. Having a scientific and methodological tool for assessing the effectiveness of interfaces, we can analyze them for the presence of various defects. Currently, there is no comprehensive tool for assessing the effectiveness of interfaces in the scientific literature. The purpose of the work is to develop evaluation tools that allow assessing the effectiveness of software product interfaces in numerical form. Methods: to achieve the stated goal, a comparative analysis of existing quantitative methods, metrics and laws from the scientific literature and international standards for software design and their software interfaces was carried out. Novelty: in comparison with existing methods, the developed approach is presented in the form of an algorithm capable of calculating indicators in the direction of the effectiveness of the compositional equilibrium of graphical user interfaces, which has not previously been evaluated by other researchers. Result: an algorithm has been developed for assessing the effectiveness of the compositional balance of graphical user interfaces, which allows for the evaluation and comparison of software products in this area.

Investigating the central place theory using trajectory big data

The human settlement system is central to land use, infrastructure development, and environmental impacts. Although central place theory (CPT) was proposed about 90 years ago and has been extensively examined by many researchers, to what extent CPT can explain the current rural settlement system in the changing age of informatization and geospatial reconstruction remains to be explored. This paper aims to contribute fresh evidence for settlement systems and examine the applicability of CPT's quantitative laws by using the trajectory data of 2.0362 billion trips from 37.53 million mobile phone users in China's Jing-Jin-Ji region (218,000 km2 area). We found that the settlement system's distribution patterns and service range conformed with the hierarchical law in CPT. However, the former was closer to the administrative principle (K = 7) in Christaller's theory, while the latter was nearer to the marketing principle (K = 3). The basic service range of all levels of settlements for rural residents was approximately 3 km, which was reflected by the rural residents' 3 km travel volume peak point. When exceeding this distance, the relationship between travel volume and distance distribution changed from linear increase to power-law attenuation. The traditional three principles of CPT influenced the settlements’ service range and K value. Nevertheless, the specific roles of the influencing factors varied in space. The findings of this paper would enhance our knowledge of CPT and settlement systems in the context of a fast growing and rapidly urbanizing society.

Modeling and analysis of droplet deposition behavior: From the micro and macro perspectives

The variation of relevant parameters during the spraying process will affect the droplet deposition behavior (DDB) on the plant leaf surface. Hence, a comprehensive analysis and modeling are the basis for model-based control design and performance optimization of spraying efficiency. This paper adopted the method of computational fluid dynamics (CFD) to conduct real-time visualization analysis and numerical modeling establishment of the DDB from the micro and macro perspectives, aiming to obtain the quantitative deposition laws of relevant parameters in the deposition process. The micro results showed that the droplet had different degrees of deposition, bouncing, and diffusion at different blade inclination angles (IAs) and contact angles (CAs). The system’s total pressure presented a consistent trend, while there was a sharp increase of about 2–3 times at the moment of impact on the leaf surface. Numerically, the droplet diffusion speed was basically at 5–7 mm/ms. And it presented an exponential function between the diffusion time and the diffusion velocity of the droplets, whose coefficient of determination (R2) equaled 0.73. The DDB of macro analysis clearly explained the change laws of droplet size, residence time, shear stress, and spreading speed. And the mathematical models of the droplet deposition thickness (DDT) on the target surface about time, spraying speed, liquid density, and fluid viscosity were established, which showed a trend of string functions. The growth rate of DDT reached a maximum of 13331% at 40 ms, which could be considered as an economic spraying time. The study achieved a comprehensive dynamic visualization and model-building of relevant spraying parameters and provided an actual reference for the spraying deposition control design and the parameters selection.

A force-based model for adaptively controlling the spatial configuration of pedestrian subgroups at non-extreme densities

The study of crowd dynamics has provided new insights into the understanding of human collective motion. However, most previous studies treated large-scale crowds as consisting of isolated individuals, but ignored the fact that pedestrian subgroups are prevalent in reality. With the increasing advancement of computer simulations, the critical role of subgroups in crowd modeling has been gradually recognized. Here, we develop a force-based model to reproduce the walking behaviors of pedestrian subgroups, in which the quantitative laws extracted from public datasets are incorporated for controlling their spatial configurations at different non-extreme densities. Numerical simulations indicate that our model achieves the simulation of pedestrian subgroups that coincides with empirical observations, and presents better simulation performance than existing subgroup models. The presence of pedestrian subgroups has also been confirmed to have certain effects on both fundamental diagrams and lane formation. Overall, this paper contributes a valuable framework to the modeling of pedestrian subgroups for guiding relevant implementations in potential application areas.

Mechanical Performance Study of Pipe-Liner Composite Structure Based on the Digital Image Correlation Method

Repair of reinforced concrete drainage pipes is often performed using polyethylene (PE) lining. To investigate the bearing capacity characteristics of a repaired composite structure, this study conducted experiments on three groups, namely, PE pipes, reinforced concrete pipes, and composite-reinforced concrete PE pipes (count = 9). The cracking and ultimate loads of the three groups under plate loads were evaluated and analyzed. A displacement monitoring method based on two-dimensional digital image correlation (2-D-DIC) and three-dimensional digital image correlation (3-D-DIC) techniques is proposed, and the quantitative laws of strain distribution at the end face of the specimen are obtained. Furthermore, the damage mechanism of the reinforced concrete pipe and the interface spalling damage mechanism of the composite-reinforced concrete PE under load were investigated to reveal the effect of PE lining improvement on the bearing capacity of the reinforced concrete pipe. The maximum deviation of the specimen vertical displacement results obtained using the new noncontact 3-D-DIC method is 2.6% compared with that of the traditional physical sensor method, and this method can successfully capture the deformation and strain data of the target specimen. Therefore, the noncontact DIC method has a broad application prospect in municipal pipeline early warning monitoring systems.

Research on laser spot location accuracy of low-power laser diode source applied to high precision laser measurement system

The results of laser spot location have an important influence on the accuracy of a laser measurement system. Laser diode (LD) sources have been widely used in recent years because of its low cost and easy integration. Based on the low-power LD source, a conventional laser spot location system was built to study the factors that affect the accuracy of location. We analyzed the influencing factors on laser spot location from two aspects of LD driven and charge coupled device (CCD) imaging, and experiments were conducted to further obtain quantitative analysis results and laws on different influencing factors, including the LD temperature, LD injection current, the size of imaging laser spot and its intensity fluctuation. The drifting RMS and the dithering range R were adapted to evaluate the drift and dither of the laser spot respectively, and the influence laws of location error were discussed. Finally, laser triangulation displacement sensor was taken as an optimization design example when considering the influencing factors studied in this paper. As a result, the RMS accuracy of the design example was 3.6 μm and its repeatability was 2.17 μm. The experimental results provided guidance for the optimization design of laser spot location measurement system.

Development of drift-flux correlations for vertical forward bubble column-type gas-liquid lead-bismuth two-phase flow

Bubble columns represent an extreme case of gas-liquid two-phase flow, where net liquid velocity is zero and the gas simply bubbles up through the liquid. The bubble column-type gas-liquid metal two-phase flow always appears in an accident scenario for pool-type lead-bismuth eutectic cooled fast breeder reactors. To accurately predict the void fraction for the accident evaluation and design of a reactor system, nine existing drift-flux type constitutive correlations are evaluated with a nitrogen-liquid heavy metal two-phase flow test. Few correlations give a relatively good prediction and the basic assumption in the distribution parameter calculation is not applicable for a bubble column. To solve this problem, analysis based on Clark’s theoretical model is carried out. The results show that the distribution parameter assumes very high values at a low Re number. As the Froude number increases, the distribution parameter tends to decrease. At lower void factions, the distribution parameter is also assumed to be at high values. This indicates that the pipe size, flow rate, and void fraction can all influence the distribution parameter. Considering the quantitative laws of these influence factors obtained by theoretical analysis and fitting the data of Ariyoshi’s test, a new correlation for a bubble column-type gas-LBE two-phase flow is developed and evaluated. The results of the statistical analysis show that the new correlation gives the best prediction for gas-LBE two-phase flow in the void fraction range of 0.018–0.313.

Desensitization effect of chemically induced coal components at room temperature: An experimental study

This study was conducted to address the rock burst problem caused by serious stress concentrations in coal seams. Based on the principle of inducing agent corrosion affecting coal components to soften coal, different inducers were selected to study the desensitization effect of acid leaching induction on coal components. The microscopic behavior characteristics of coal under acid leaching were analyzed, and the qualitative and quantitative laws were obtained for different acid leaching times and microscopic behavior characteristics. The results show the following: (1) The mixed acid solution as an inducer has the effect of immersion, dissolution, and fracture on coal. During the reaction process, the internal pores of the coal expand, and the height of the external liquid decreases. The mixed acid solution had the best effect in terms of the removal of minerals in coal. (2) Under microscopic conditions, the internal crack width of the coal body expanded several times after mixed acid soaking; the difference in the unevenness before and after compression fracture was stable at 25–27%, and the mixed acid expanded the gap in the coal. (3) This practical study shows that the characterization changes of the mixed acid solution, injected into the borehole, combines the characteristics of the citric acid and phosphoric acid solution. The minerals around the borehole are dissolved, and the debris fuses with the solution. The liquid is viscous and forms a film on the surface of the solution. The mixed acid has a more obvious effect on the immersion and dissolution of coal.

Study on oxidation-creep behavior of a Ni-based single crystal superalloy based on crystal plasticity theory

Long-term high temperature oxidation seriously affects the creep properties of the Ni-based single crystal superalloy. By using experimental research together with finite element simulation, the effects of high temperature oxidation on creep properties of a Ni-based single crystal superalloy (Ni-9.0Co-4.0Cr-5.7Al-7.0Ta-8.0W-2.2Re, wt.%) were studied. The specimens were pre-oxidized at 1100 °C for different periods of time, and then the pre-oxidized specimens were conducted by creep tests at 980 °C/270 MPa. By data fitting and analysis, the thickness evolution law and dynamic model of oxide layer/heat affected layer were established and the quantitative effect laws of pre-oxidation on creep life and deformation were established. The evolution and influence mechanism of oxide layer, heat-affected layer and substrate on creep failure were systematically studied by scanning electron microscope combined with energy dispersive spectrum analysis (SEM-EDS). Based on the thickening dynamic model of heat-affected layer and crystal plasticity theory, two oxidation-creep models were established. The initial damages caused by oxidation and microstructure evolution are both considered in the initial pre-oxidation damage model, which is fast and efficient. The distribution and evolution of stress, strain, resolved shearing stress and strain of the substrate and the heat-affected layer are obtained by another model, the two-phase model. The two models are compared and analyzed, which is also the uniqueness and innovation of this study. The simulations results of the two models are in good agreement with the creep tests.

Scaling of the strange-metal scattering in unconventional superconductors.

Marked evolution of properties with minute changes in the doping level is a hallmark of the complex chemistry that governs copper oxide superconductivity as manifested in the celebrated superconducting domes and quantum criticality taking place at precise compositions1-4. The strange-metal state, in which the resistivity varies linearly with temperature, has emerged as a central feature in the normal state of copper oxide superconductors5-9. The ubiquity of this behaviour signals an intimate link between the scattering mechanism and superconductivity10-12. However, a clear quantitative picture of the correlation has been lacking. Here we report the observation of precise quantitative scaling laws among the superconducting transition temperature (Tc), the linear-in-T scattering coefficient (A1) and the doping level (x) in electron-doped copper oxide La2-xCexCuO4 (LCCO). High-resolution characterization of epitaxial composition-spread films, which encompass the entire overdoped range of LCCO, has enabled us to systematically map its structural and transport properties with unprecedented accuracy and with increments of Δx = 0.0015. We have uncovered the relations Tc ~ (xc - x)0.5 ~ (A1□)0.5, where xc is the critical doping in which superconductivity disappears and A1□ is the coefficient of the linear resistivity per CuO2 plane. The striking similarity of the Tc versus A1□ relation among copper oxides, iron-based and organic superconductors may be an indication of a common mechanism of the strange-metal behaviour and unconventional superconductivity in these systems.

Formation of organic chloride in the treatment of textile dyeing sludge by Fenton system

In the oxidation treatment of textile dyeing sludge, the quantitative and transformation laws of organic chlorine are not clear enough. Thus, this study mainly evaluated the treatment of textile dyeing sludge by Fenton and Fenton-like system from the aspects of the influence of Cl−, the removal of polycyclic aromatic hydrocarbons (PAHs) and organic carbon, and the removal and formation mechanism of organic chlorine. The results showed that the organic halogen in sludge was mainly hydrophobic organic chlorine, and the content of adsorbable organic chlorine (AOCl) was 0.30 mg/g (dry sludge). In the Fenton system with pH=3, 500 mg/L Cl−, 30 mmol/L Fe2+ and 30 mmol/L H2O2, the removal of phenanthrene was promoted by chlorine radicals (•Cl), and the AOCl in sludge solid phase increased to 0.55 mg/g (dry sludge) at 30 min. According to spectral analysis, it was found that •Cl could chlorinate aromatic and aliphatic compounds (excluding PAHs) in solid phase at the same time, and eventually led to the accumulation of aromatic chlorides in solid phase. Strengthening the oxidation ability of Fenton system increased the formation of organic chlorines in liquid and solid phases. In weak acidity, the oxidation and desorption of superoxide anion promoted the removal and migration of PAHs and organic carbon in solid phase, and reduced the formation of total organic chlorine. The Fenton-like system dominated by non-hydroxyl radical could realize the mineralization of PAHs, organic carbon and organic chlorines instead of migration. This paper builds a basis for the selection of sludge conditioning methods.

Extension knowledge representation of evolutionary law of technological systems in TRIZ

Due to lack of formal and quantitative evolutionary laws, current technology systems in TRIZ can hardly be used in intelligent innovation design. To this end, an Extenics-based method is proposed in this work, which formally expresses the extension knowledge implied in the evolutionary law of technology systems. Based on domain knowledge, extension model, extension rules, extension transformation, and transformation rules, etc., the general steps of extension knowledge representation of evolutionary law of technology systems are studied. Taking evolution law to super system as an example, the corresponding extension knowledge is established. Research results suggest that the proposed method is able to clearly express the connotation and extension of the evolutionary laws of technology systems, thus paving a way applying these laws to extension intelligent design. Application outcomes on the dust removal and spraying system in coal preparation plant validates the effectiveness of the proposed method.

Zoning of mutual influence of approach rock tunnels based on a safety factor

For multiple approach tunnels, the construction of the new tunnel near the existing tunnel modifies the state of stresses and movements around the existing tunnel in an area called the “influence zone”. In this study, new method is developed to optimize the relative position of approach tunnels and guide their design via the zoning of mutual influence of the approach tunnels based on a safety factor. The strength reduction method is applied to calculate the global safety factor of multiple approach tunnels in limit state. According to quantitative laws of variation in the safety factor from single tunnel to multiple tunnels, the strong influence, weak influence, and no influence have been zoning to guide the design and construction of approach tunnels. By changing the relative position of the new tunnel complex, the safety factor and failure shapes of the tunnel complex in several cases are obtained through numerical simulation. The results are based on dividing the influence zone of approach construction of the new tunnel complex. Combining the influence zone with failure shapes, the relative position of the tunnel complex is optimized. Special support countermeasures for weak tunnel complex parts and parameters of support are initially determined.

Pressure distribution feature-oriented sampling for statistical analysis of supercritical airfoil aerodynamics

In the field of supercritical wing design, various principles and rules have been summarized through theoretical and experimental analyses. Compared with black-box relationships between geometry parameters and performances, quantitative physical laws about pressure distributions and performances are clearer and more beneficial to designers. With the advancement of computational fluid dynamics and computational intelligence, discovering new rules through statistical analysis on computers has become increasingly attractive and affordable. This paper proposes a novel sampling method for the statistical study on pressure distribution features and performances, so that new physical laws can be revealed. It utilizes an adaptive sampling algorithm, of which the criteria are developed based on Kullback–Leibler divergence and Euclidean distance. In this paper, the proposed method is employed to generate airfoil samples to study the relationships between the supercritical pressure distribution features and the drag divergence Mach number as well as the drag creep characteristic. Compared with conventional sampling methods, the proposed method can efficiently distribute samples in the pressure distribution feature space rather than directly sampling airfoil geometry parameters. The corresponding geometry parameters are searched and found under constraints, so that supercritical airfoil samples that are well distributed in the pressure distribution space are obtained. These samples allow statistical studies to obtain more reliable and universal aerodynamic rules that can be applied to supercritical airfoil designs.

Cellular resource allocation strategies for cell size and shape control in bacteria.

Bacteria are highly adaptive microorganisms that thrive in a wide range of growth conditions via changes in cell morphologies and macromolecular composition. How bacterial morphologies are regulated in diverse environmental conditions is a long-standing question. Regulation of cell size and shape implies control mechanisms that couple the growth and division of bacteria to their cellular environment and macromolecular composition. In the past decade, simple quantitative laws have emerged that connect cell growth to proteomic composition and the nutrient availability. However, the relationships between cell size, shape, and growth physiology remain challenging to disentangle and unifying models are lacking. In this review, we focus on regulatory models of cell size control that reveal the connections between bacterial cell morphology and growth physiology. In particular, we discuss how changes in nutrient conditions and translational perturbations regulate the cell size, growth rate, and proteome composition. Integrating quantitative models with experimental data, we identify the physiological principles of bacterial size regulation, and discuss the optimization strategies of cellular resource allocation for size control.

Investigating the effect of acid erosion on degradation and brittle fractures in coal using etching solutions

ABSTRACT With an increase in the application of deep coal mining, there has been a significant increase in the risk of rock bursts due to increased mine pressures. Thus, research is required on more effective methods of preventing and controlling rock bursts. In this study, three types of solutions were used to study the brittle fracture degradation of coal by acid leaching. The principle of acid leaching and the microscopic mechanical behavior characteristics of brittle fracture degradation were analyzed. The quantitative laws governing different acid leaching times and unloading values were then obtained. The results were as follows. (1) The iron ions in the coal were replaced by a citric acid solution. The scanning electron microscope (SEM) results of the damaged coal sample indicated slight bending of the coal surface, accompanied by the shedding of small coal particles. After immersion, the failure strain increased by 63.6%, and the failure response time increased by 324.1%. (2) After soaking the coal sample in a phosphoric acid solution, numerous bubbles were observed on the coal surface, and the permeability was significantly enhanced. The SEM results of the damaged coal revealed that the coal surface was divided into blocks after soaking, and the minerals in the coal precipitated and accumulated. After immersion, the failure stress decreased by 24.5%. (3) A mixed acid solution, comprising citric and phosphoric acids, resulted in the most significant corrosion effect. The SEM results of the damaged coal revealed that chemical reactions occurred after the soaking process, and minerals were precipitated. Furthermore, uniaxial failure was the most complete. In particular, the failure stress decreased by 49.8%, the failure strain increased by 81.8%, and the failure response time increased by 77.7%. The mixed acid solution enhanced the plastic characteristics of the coal, reduced its strength, and demonstrated favorable characteristics for coal pressure relief. Thus, the results of this study provide significant engineering advancements for chemical pressure reduction technology, which can be applied to deep coal mining.

Parametric sensitivity analysis of Aerodynamic stability for planar membrane structures

To explore the influence of design parameters on the aerodynamic stability of planar membrane structures, a mathematical model for calculating the critical wind speed of flat panel structures was established, and the closed expression of the critical wind speed was obtained through the criterion of instability. The influence of membrane size, membrane density, pretension and other parameters on the critical wind speed was studied by monofactor analysis. The results show that, with the help of the new concept of benefit loss coefficient, the sensitivity analysis of instability critical wind speed parameters can be easily carried out, and many qualitative and quantitative laws can be obtained.

The roles of T cell competition and stochastic extinction events in chimeric antigen receptor T cell therapy.

Chimeric antigen receptor (CAR) T cell therapy is a remarkably effective immunotherapy that relies on in vivo expansion of engineered CAR T cells, after lymphodepletion (LD) by chemotherapy. The quantitative laws underlying this expansion and subsequent tumour eradication remain unknown. We develop a mathematical model of T cell–tumour cell interactions and demonstrate that expansion can be explained by immune reconstitution dynamics after LD and competition among T cells. CAR T cells rapidly grow and engage tumour cells but experience an emerging growth rate disadvantage compared to normal T cells. Since tumour eradication is deterministically unstable in our model, we define cure as a stochastic event, which, even when likely, can occur at variable times. However, we show that variability in timing is largely determined by patient variability. While cure events impacted by these fluctuations occur early and are narrowly distributed, progression events occur late and are more widely distributed in time. We parameterized our model using population-level CAR T cell and tumour data over time and compare our predictions with progression-free survival rates. We find that therapy could be improved by optimizing the tumour-killing rate and the CAR T cells' ability to adapt, as quantified by their carrying capacity. Our tumour extinction model can be leveraged to examine why therapy works in some patients but not others, and to better understand the interplay of deterministic and stochastic effects on outcomes. For example, our model implies that LD before a second CAR T injection is necessary.

Effect of Expansion Ratio and Wall Thickness on Large-Diameter Solid Expandable Tubular After Expansion

Abstract The large-diameter solid expandable tubular (SET) with a smaller wall thickness faces the risk of internal pressure burst and external squeeze collapse in repairing damaged casing well. The internal pressure and external squeezing resistance calculation of the tubes using the analytical method require many expansion experiments and postexpansion tensile experiments, resulting in high costs and low efficiency. This paper gives a set of laboratory expansion and postexpansion performance test, which is based on the laboratory experiment and mechanical properties of material expansion. Two materials are studied: 316 L and 20G. Then it analyses the error and causes of the error in the traditional analytical algorithm. Besides, it establishes an accurate finite element (FE) model to study the quantitative influence of expansion ratio and wall thickness on the burst strengths and collapse strengths of the tube. The results show that the toughness and hardening ratio of 316 L is better than 20G at the same expansion ratio. The numerical simulation results of the model can effectively simulate the expansion process and the mechanical properties of SET in good agreement with the laboratory test results. The expansion ratio and wall thickness affect the mechanical properties after expansion. Thus the quantitative laws of the expansion driving force, internal pressure resistance, and external squeezing resistance under different variables are summarized. To ensure the integrity of the reinforced wellbore, the expansion ratio should not exceed 12.7%. The current study lays a theoretical basis and technical support for optimizing SET and preventing downhole accidents.

Sudden freezing and thawing of entanglement sharing in a shrunken volume

Within the one-excitation context of two identical two-level atoms interacting with a common cavity, we examine the dynamics of all bipartite one-to-other entanglements between each qubit and the remaining part of the whole system. We find a new non-analytic "sudden" dynamical behavior of entanglement. Specifically, the sum of the three one-to-other entanglements of the system can be suddenly frozen at its maximal value or can be suddenly thawed from this value in a periodic manner. We calculate the onset timing of sudden freezing and sudden thawing under several different initial conditions. The phenomenon of permanent freezing for entanglement is also found. We also identify a non-trivial upper limit for the sum of three individual entanglements, which exposes the concept of entanglement sharing in a shrunken "volume". Further analyses about freezing and thawing processes reveal quantitative and qualitative laws of entanglement sharing.