Law Of Expansion Research Articles

Criterion for hydraulic fracture propagation behaviour at coal measure composite reservoir interface based on energy release rate theory

In this study, a discriminative model of fracture expansion through a composite reservoir interface was established. During fracture transformation, the model, based on the theory of energy release rate at the fracture tip, helps clarify the critical conditions and assess the law of hydraulic fracture expansion through coal composite reservoir interfaces. This model considers shear and tensile processes during fracturing at the coal–rock interface and the effects of interface material property differences on fracture extension. In addition, fracture extension pattern differentiation is achieved by comparing the hydraulic fracture tip penetration and bending energy release rates (Gp/Gd) with the ratio of reservoir fracture and interface fracture energies (ΓR/ΓF). The accuracy of this discriminant criterion was verified by comparing the predicted results of the discriminant model with fracturing test results under identical conditions. The effects of various factors on Gp/Gd and hydraulic fracture penetration extension were investigated by using the sand-mudstone composite reservoir of the Shibox Formation in the Linxing Block, China, as the geological background. The results indicate that for certain values of ΓR/ΓF, Gp/Gd increases logarithmically with an increase in water pressure in the wellbore. Moreover, the difference in ground stress and elastic modulus between the layers exponentially increases with increasing Poisson’s ratio difference and the angle between fracture and interface and decreases logarithmically with increasing fracture height. These results indicate that hydraulic fractures are likely to penetrate from reservoirs with a high elastic modulus and Poisson’s ratio into reservoirs with a low elastic modulus and Poisson’s ratio. Furthermore, hydraulic fractures are likely to penetrate formations with large differences in pinch angle and ground stress. Under specific geological conditions, high water pressure in the wellbore and small seam height are favourable for fracture penetration.

Laws of macroevolutionary expansion

Van Valen’s law of constant extinction postulates that in comparable ecological contexts, the probability for a taxon to survive to the next time interval is independent of how long it has already existed. The law implies that species do not age, that is, the survival probability from one time step to the next does not decrease with species’ age. While the original law describes survivorship over time, here we show that there is a counterpart to the law describing species dynamics in space. Indeed, the probability for a taxon to expand a step further in its range size does not depend on how large of a range the taxon already occupies. We show that such patterns of stochastically constant expansion are common in the global mammalian fossil record throughout the Cenozoic and are consistent with the mammalian species distribution in the present-day world. Intriguing is that the law in space holds best for the linear dimension of the range rather than for the range area. We interpret this as suggesting that species primarily expand via the frontier of their range; this process is known as leading-edge expansion in ecology. And while the difficulty of expanding in linear steps remains constant, the area gains diminish. In line with evolutionary theory collectively known as the Red Queen’s hypothesis, this suggests that the effectiveness of expansion saturates, even if species longevity does not. When interpreted in reverse, this explains from the macroevolutionary perspective why larger species ranges are associated with lower extinction risks.

Analysis of mechanical response mechanism and energy evolution characteristics of saturated coal with a single pre-existing hole

It is essential to elucidate the mechanical mechanism of water injection and large-diameter drilling pressure relief measures on coal rock deformation and failure. This helps coal mines adopt more precise and effective dynamic disaster prevention and control measures. To obtain the mechanical response mechanism and energy evolution characteristics of saturated coal with a single pre-existing hole, uniaxial compression tests was carried out, and the deformation and failure process of coal samples were monitored by high-speed camera and acoustic emission monitoring systems. It is found that water saturation, single pre-existing hole measures, and their coupling effect resulted in a deterioration in the coal sample's strength by approximately 23.49%, 9.47%, and 47.95% respectively. The final failure mode of coal samples with different measures is shear failure. The law of fracture development and expansion and energy accumulation and release in different coal samples is roughly the same, the speed of energy accumulation and release in different stages is different. Water saturation and single pre-existing hole measures can affect the impact risk of coal samples, and water saturation can significantly reduce the impact tendency of coal samples, and reduce the impact energy index of complete coal samples by 56.59%. The impact tendency index of natural coal sample is slightly increased by single pre-existing hole measure, and the impact energy index of intact coal sample is reduced by 46.78% by the coupling of the two measures. These findings can provide technical support for coal mine power disaster prevention and control.

Mechanism of interface debonding in steel-concrete components caused by thermal expansion and contraction

The steel tube concrete structure constrains the core concrete through the inner wall of the steel tube, forming a hoop effect, significantly improving the compressive performance of the core concrete and effectively exerting the tensile performance of the steel tube. Although this structure has been optimized in terms of mechanical properties, its ultra-high bonding performance makes it extremely difficult to disassemble and recycle. To explore ways to solve this challenge, this article selects C40 concrete as the matrix concrete, and designs and produces circular steel tube concrete specimens and square steel tube concrete specimens with a height of 250mm and a steel tube wall thickness of 4mm. The specific research content covers the hoop effect of steel pipes on core concrete, the degradation law of thermal expansion and contraction interface bonding performance of steel pipe concrete components, the coupling effect of cutting joints and thermal expansion and contraction on interface bonding performance of steel pipe concrete components, and the mechanism of interface debonding of steel pipe concrete components. Through systematic experiments and analysis, the influence of different variation parameters on the debonding performance of steel tube concrete was deeply studied, and its debonding mechanism was revealed. This series of studies provides an important scientific basis for the theoretical understanding and application of steel-concrete structures, helping to overcome the problem of dismantling and recycling, and promoting the transformation and development of related equipment.

Friedrich Ratzel’s Law of the Spatial Growth of States in the Situation of the New World Order Formation

In this paper, on the basis of an institutional approach, it is analyzed how fair the “law of expansion” of F. Ratzel is in the current situation of the formation of a new world order. It is shown that in modern conditions the instinct of self-preservation induces social systems not to territorial expansion due to an increase in the occupied geographical space, but to integration in various forms, which is based on a single normative approach to the mechanisms of the functioning of the union. In this sense, integration is a kind of expansion of the space occupied by society. Integration unions can increase, but up to a certain limit (saturation limit), determined not by the boundaries of geographical space, but by the possibility of developing a common position on the main issues of functioning, common norms and practices. As a rule, alliances are not absolutely symmetrical and include the “core” and the periphery of integration. The former include the most economically and politically strong states. At the same time, due to the asymmetry of the unions, the “core” institutions are transplanted to the periphery and there is a bidirectional institutional diffusion, which is due to the desire for institutional convergence, and this facilitates interaction within the union. Thus, “channels” for the institutional expansion of integrable societies are formed within the unions. Transplantation and diffusion of institutions are the mechanisms for the implementation of expansion in modern conditions. It is shown that when integrating social systems in order to mitigate possible institutional imbalances, the action of institutions that are complementary to the dominant ones in the institutional matrix is included: when integrating X-matrix countries - market ones, and vice versa.

Five - Dimensional Plane Symmetric Cosmological Model with Quadratic Equation of State in f(R,T) Theory of Gravity

In this paper, we analysed the five-dimensional plane-symmetric cosmological model containing perfect fluid in the context of f(R, T) gravity. Field equations have solved for two class of f(R, T) gravity i.e., f(R, T) = R + f(T) and f(R, T) = f1(R)f2(T) with the inclusion of cosmological constant Λ and quadratic equation of state parameters in the form p = αρ2 − ρ, where α is a constant and strictly α≠ 0. In order to derive the exact solutions, we utilize volumetric power law and exponential law of expansion. The physical and geometrical aspects of model have discussed.

Spatio–temporal dynamics and human–land synergistic relationship of urban expansion in Chinese megacities

Megacities play important roles in countries' politics, economy, culture, etc. Exploring the law of urban expansion of megacities has important reference for sustainable urbanization. Here, the spatiotemporal dynamics of urban expansion were quantified analyzed in 21 Chinese megacities from 2000 to 2020 with quantitative measurement indicators and explored the human–land synergistic relationship used the decoupling model. Results are as follows: (1) China's megacities experienced significant expansion, and urban expansion characterized as rapid initially but slowed down thereafter. (2) Urban expansion in megacities was characterized as having significant spatial differences, and rapidly expanding megacity centers moved from eastern to midwestern China. (3) Urban spatial expansion of megacities was mainly an enclave type in 2000–2010 and marginal type in 2010–2020. (4) The main type of human–land synergistic relationship in megacities were weak decoupling, there is a significant increase in expansive coupling and expansive negative decoupling in 2010–2020; (5) Lastly, human–land synergy relationship in most megacities was uncoordinated based on the per capita urban land area and decoupling type. The findings of this study can deepen the understanding of the characteristics and quality of urbanization evolution, and provides reference for high-quality development planning and decision-making in megacities.

Quantitative law and scenario-based forecasting of different land use expansion, based on reliability analysis in mountainous areas.

The continuous high-intensity and disorderly expansion of construction land in mountainous areas threatens city development; consequently, the scientific guidance of its sustainable development has become a research hotspot. This work aimed to develop a new theoretical framework for predicting land expansion. Based on DMSP/OLS-Landsat 7 data correction from 2000 to 2019, to ensure data reliability, this study quantitatively analysed the expansion law of land-use and land-cover (LULC) in Huayuan, a typical mountainous area in China. Based on the land expansion law, the patch-generating land use simulation (PLUS) model was used to predict various types of LULCs in different scenarios. The results showed that (1) the reliability of LULC under multi-source spatio-temporal data correction reached more than 0.97. (2) The expansion law of industrial and mining land, urban living land, and traffic land is sprawl, while rural living land is enclaved and the expansion direction and intensity are obviously different. (3) The scale of land expansion in the natural-oriented scenario was significantly higher than that in the humanism-oriented scenario, with a higher value of 199.33 hm2. This study expands the case study of land use analysis and prediction, and provides scientific guidance for different land expansion planning, which can avoid the mismatch and waste of land resources. Furthermore, it also deepens the exploration of LULC identification reliability method and enriches the theory of different land use prediction in mountainous areas.

Morphoelastic modelling of pattern development in the petal epidermal cell cuticle.

We use the model system Hibiscus trionum as a vehicle to study the origin and propagation of surface nano-ridges in plant petal epidermal cells by tracking the development of the cell shape and the cuticle. In this system, the cuticle develops two distinct sub-layers, (i) an uppermost layer which increases in thickness and in-plane extension and (ii) a substrate, composed of cuticular and cell wall material. We quantify the pattern formation and geometrical changes and then postulate a mechanical model assuming that the cuticle behaves as a growing bi-layer. The model is a quasi-static morphoelastic system and it is numerically investigated in two- and three-dimensional settings, using different laws of film and substrate expansion and boundary conditions. We recreate several features of the observed developmental trajectories in petals. We establish the respective roles of the layers' stiffness mismatch, the underlying cell-wall curvature, the cell in-plane expansion and the thickness growth rates of the layers in determining the observed pattern features, such as the variance observed in the amplitude and wavelength of the cuticular striations. Our observations provide evidence which justifies the growing bi-layer description, and provide valuable insights into why some systems develop surface patterns and others do not.

The structure of the radiation field of a symmetric slot line perpendicular to the edge of an infinite half-plane, taking into account the cross-polarization component

Background. Symmetric slot lines on a perfectly reflecting half-plane are good mathematical models for slot antennas on an ideal plane of finite dimensions, which in practice have a high gain and operate over a wide frequency band. These antennas are used in ultra-fast information processing systems based on microwave and optical volume integrated circuits. Aim. The work presents a solution to the problem of radiation of a perfectly reflecting half-plane, which was excited by a symmetric slot line with a different law of slot expansion. Methods. The problem was solved by the Fourier variable separation method, by which the Green tensor function was obtained, which connects the two components of the antenna radiation field with the excitation field in the gap. Results. It is shown that in the far zone, the radiation field of an ideally reflecting half-plane has two components: the main and crosspolarization. The Green tensor function has a complex form and consists of two terms. The analysis of the Green tensor function shows the participation of each term in the formation of a field in the far zone, demonstrates the mechanism of radiation and leads to known special cases for slot radiators. Conclusion. The validity of the presented mathematical model is confirmed by experimental research.

Meso-damage analysis of concrete based on X-ray CT in-situ compression and using deep learning method

Traditional concrete failure research mostly based on surface cracks to analyze its macro mechanical properties, which cannot obtain the internal structure and failure process on a mesoscopic level. The internal topography of concrete can be acquired by using X-ray CT to scan the entire concrete specimen, and the internal structure change caused by stress can be captured when combined with an in-situ CT loading device. Thus, in-situ X-ray computed tomography (X-ray CT) scanning was performed on concrete under uniaxial compression, and the real-time CT images of the meso-damage evolution process inside concrete were obtained. Deep Learning method was applied to extract two-dimensional (2D) and three-dimensional (3D) cracks for visual analysis and quantitative characterization. The damage evolution process, damage variables and Poisson's ratio of concrete were analyzed based on CT values. The results revealed that crack formation and propagation did not necessarily occur at the interface, the low-density area was prone to cause concrete damage. The crack morphology obtained by deep learning was highly consistent with the distribution of cracks in concrete. The law of crack extension, distribution and expansion could be represented through crack thickness, crack voxel number and crack area. The initial meso-damage distribution of concrete had an important impact on the occurrence of localized damage. The results of CT value showed that the meso-damage of concrete develops from inside-out. The damage evolution process was divided into compression stage Ⅰ, damage stage Ⅱ and destruction stage Ⅲ. The damage variable and Poisson's ratio were evaluated by CT value could further characterize the deterioration degree of concrete.

Study on the Influence of Saturation on Freeze–Thaw Damage Characteristics of Sandstone

In order to explore the evolution mechanism of freeze-thaw disasters and the role of water in the freezing-thawing cycles of rocks, the macro mechanical indexes and microstructural characteristics of seven different saturation sandstones after certain freeze-thaw cycles were analyzed. Electron microscope scanning, nuclear magnetic resonance, and uniaxial compression tests were employed to study the migration law of water in the rock, the crack growth law, and the damage mechanism during freeze-thaw cycles. The results showed that when the saturation was 85%, the peak load curve of sandstone with different saturation appeared at the minimum point, and the porosity of sandstone reached the maximum. The damage variable increased sharply when the saturation was 75-85%. This proves that 85% saturation is the critical value of sandstone after five freeze-thaw cycles. The water migration freezing model is established, and the migration direction of capillary film water during freezing is micropore → mesopore → macropore. The migration of water is accompanied by the expansion and generation of cracks. Then we study the mechanism and law of crack expansion, and the crack propagation rate is positively related to the theoretical suction. The theoretical suction and theoretical ice pressure increased linearly with the decrease in temperature, which accelerated the crack propagation. The crack propagation rate in decreasing order is Vmacropore > Vmesopore > Vmicropore. The research results can provide a theoretical basis for evaluating the stability of rocks under the action of freeze-thaw cycles in cold regions.

A velocity model in the wake of a thin plate parallel to uniform flow

A novel equation of wake model for the wake velocity distribution of a flat plate is proposed and verified in this study. The core of this equation is a special dimensionless method of the velocity deficit and the distance from the trailing edge of the plate along the flow direction, and a dimensionless standard deviation satisfying the law of linear expansion. In this study, it is assumed that the velocity deficit in the wake has a self-similar Gaussian distribution. Moreover, another conservation of momentum and Blasius equation is applied. The velocity distribution expression comprises the near-wake region and the far-wake region in accordance with the standard deviation of the Gaussian distribution. The model is capable of accurately predicting the velocity deficit of the near wake velocity distribution, and the dimensionless standard deviation serves as the only model parameter. The proposed model is compared with the existing research and present water-tunnel measurements, such that they are well consistent with each other.

Simulation study on the deflection and expansion of hydraulic fractures in coal-rock complexes

The physical difference and structural weak surface of coal-rock complexes greatly influence the morphology of hydraulic fractures (HFs). This study aims to explore the law of deflection and expansion of HFs in coal-rock complexes under different stress conditions. First, a theoretical model for HF deflection in coal-rock complexes was derived. Besides, a numerical model for HF expansion in coal-rock complexes was established based on the traction–separation criterion, the cohesion embedding method and the finite element method for fracture expansion. With the aid of the established model, the laws of morphology and induced stress field evolutions during HF expansion were studied. The following conclusions were drawn. When the HF is closer to the interface, the effect of physical difference is more notable, and the HF is more likely to expand along the coal seam. As the difference between the maximum horizontal principal stress and the vertical ground stress decreases from 8 MPa to 0 MPa, the coal-rock complexes experience HF expansion in the horizontal direction, secondary fracture generation in the Z-axis direction, and HF deflection to the interface in the -Z-axis direction in turn. During HF expansion, a stress difference of about 19 MPa exists between the fracture tip section and the interface, which is favorable for HF initiation and expansion. The effect of physical difference between coal and rock leads to the formation of an induced stress field, which causes a 3–4 times difference in the displacement values in different areas during HF expansion. The abovementioned main causes of HF deflection can provide reference for the design and application of the hydraulic fracturing technology for complex formations with different lithologies.

The matter density PDF for modified gravity and dark energy with Large Deviations Theory

ABSTRACT We present an analytical description of the probability distribution function (PDF) of the smoothed 3D matter density field for modified gravity and dark energy. Our approach, based on the principles of Large Deviations Theory, is applicable to general extensions of the standard Lambda cold dark matter (ΛCDM) cosmology. We show that late-time changes to the law of gravity and background expansion can be included through Einstein-de Sitter spherical collapse dynamics combined with linear theory calculations and a calibration measurement of the non-linear variance of the smoothed density field from a simple numerical simulation. In a comparison to N-body simulations for f(R), DGP, and evolving dark energy theories, we find per cent level accuracy around the peak of the distribution for predictions in the mildly non-linear regime. A Fisher forecast of an idealized experiment with a Euclid-like survey volume demonstrates the power of combining measurements of the 3D matter PDF with the 3D matter power spectrum. This combination is shown to halve the uncertainty on parameters for an evolving dark energy model, relative to a power spectrum analysis on its own. The PDF is also found to substantially increase the detection significance for small departures from General Relativity, with improvements of up to six times compared to the power spectrum alone. This analysis is therefore very promising for future studies including non-Gaussian statistics, as it has the potential to alleviate the reliance of these analyses on expensive high-resolution simulations and emulators.

Exploration on the Development Boundary Delimitation Method of Small and Medium-sized Cities under Multi-scenario Simulation

Research purposes: In order to solve the problem that the development boundary of small and medium-sized cities is "inaccurate" and it is difficult to coordinate with the current land and space planning, the purpose is to form a set of universal development boundary demarcation process of small and medium-sized cities. Methods: Optimize the existing practice of demarcation research methods, fully connect with the pattern of land development and protection, combine the artificial neural network model (GEOSOS model) and use Model Builder to design a land use simulation model with "double evaluation" results and "reverse" protection red line module, and consider the policy-oriented influence, and comprehensively consider the above aspects to explore a method of boundary demarcation of urban development that is coordinated and unified with development and protection. Research: The simulated land use results of the model based on "positive development guidelines" and "reverse scale control" are in line with the law of urban spatial expansion of small and medium-sized cities represented by dangyang city. The research results can not only provide reference for the future urban development of dangyang city and the spatial planning of dangyang city, but also provide technical support for the demarcation of urban development boundaries in China.

Model Test Study on Overburden Failure and Fracture Evolution Characteristics of Deep Stope with Variable Length

Taking two typical stopes with variable length of working face inclined length from small to large and from large to small as the research object, the stope overburden structure model under different face length conditions is constructed through laboratory similar material simulation test, and the dynamic evolution laws of overburden instability deformation, unloading expansion, and collapse failure of forward and reverse knife handle stopes are analyzed. The three‐dimensional perspective technology of parallel network electrical method is used to study the spatial distribution range and fracture development characteristics of overburden internal failure. The research shows that the overburden fracture of stope with variable length has the “time‐pace‐scale” evolution effect of short‐time sudden change, zoning load transfer, and continuous extension. The evolution of roof fracture has experienced the development process of unloading expansion, tensile fracture instability, shrinkage deformation, and closure stability. The rise and fall of resistivity during mining in stope with variable length is closely related to the mining time step. When mining 40 cm, it is the position where the resistivity value changes suddenly. The rise of resistivity in the vertical direction makes the electric field show the transient response characteristics of dynamic expansion and rapid evolution. The development height of water conducting fracture zone of the reverse knife handle working face with the inclined length changing from large to small is slightly larger, the degree of overburden damage is high, and the fracture development is relatively sufficient.

On Determining the Optimal Lifting Law of the Walking Propulsion Device Foot of an Underwater Robot from the Bottom

The problem of lifting the foot of the walking propulsion device of an underwater mobile robot is considered, taking into account the additional “compression” force acting on it. A mathematical model has been developed for the detachment of a propulsion foot from the ground, based on Henry's laws establishing the concentration of dissolved air in a liquid, the law of gas expansion at a constant temperature, Darcy's law on fluid filtration and the theorem on the motion of the center of mass of a solid body. The linearized model allows to obtain and analytical solutions. Based on the solution of the variational problem, optimal modes of lifting the foot of the walking propulsion of an underwater mobile robot are established.

A novel approach for characterizing frozen soil damage based on mesostructure

In this study, the relationship between the computed tomography (CT) number and the density of frozen soil was established on a macro and mesoscopic scale, aimed at overcoming the shortcomings of the mesoscopic damage behavior predicted by previous macroscopic research on frozen soil. In addition, considering the influence of stress level and temperature, a mesoscopic structural damage variable was proposed, which could reflect the damage characteristics of frozen soil. On this basis, combining the meso-damage of frozen soil with the macro-mechanical response, the mechanism of the damage evolution of frozen soil under stress was studied. It was found that the variation law of porosity was consistent with the law of the mesoscopic damage expansion in frozen soil. In the initial stage of stress loading, compaction was observed before meso-crack expansion. The internal structure exhibited a strengthening effect, by which the damage was reduced. The macroscopic mechanical properties were characterized by an elastic strain phase. As the stress continued to increase, an inflection point of the damage value appeared, and the damage gradually increased. The starting point of the meso-fracture expansion curve could represent the stress yield point on the macroscopic mechanical curve, and also represented the inflection point of the volume change of the material from the contraction to the dilatancy. When the damage value was gradually increased and became equal to the initial value, the deviatoric stress reached the peak of the macroscopic mechanical curve.

A new method of extracting built-up area based on multi-source remote sensing data: a case study of Baoding central city, China

The accurate extraction of Built-Up Areas (BUAs) is of great significance for analysing urban spatial evolution patterns. In this study, we proposed a new method for high-precision extraction of BUA based on multi-source remote sensing data. Firstly, Built-Up Area Extraction Index (BAEI) was used to preliminarily identify the BUA based on Landsat 8 imagery. Secondly, the Support Vector Machine (SVM) algorithm was used for improving the extraction precision of BUA, whose selected training sample was established on the Nighttime Light (NTL) data. Then, images fusion and continuity correction were carried out. Finally, the Neighbourhood Statistics Analysis (NSA) was used to adjust and remove the part of the non-urban centre which was misjudged as the BUA. Our results show that this method has better performance on both overall accuracy and Kappa coefficient compared with other classic methods, which provides empirical reference for understanding law of land expansion and rational land planning.