Spatial Superposition Research Articles

Spatial Distribution of, and Variations in, Cold Regions in China from 1961 to 2019

In this study, on the basis of the temperature data collected at 612 meteorological stations in China from 1961 to 2019, cold regions were defined using three indicators: an average temperature of <−3.0 °C during the coldest month; less than five months with an average temperature of >10 °C; and an annual average temperature of ≤5 °C. Spatial interpolation, spatial superposition, a trend analysis, and a spatial similarity analysis were used to obtain the spatial distribution of the cold regions in China from 1961 to 2019. Then, the areas of the cold regions and the spatial change characteristics were analyzed. The results reveal that the average area of the cold regions in China from 1961 to 2019 was about 427.70 × 104 km2, accounting for about 44.5% of the total land area. The rate of change of the area of the cold regions from 1961 to 2019 was −14.272 × 104 km2/10 a, exhibiting a very significant decreasing trend. On the basis of the changes between 1991–2019 and 1961–1990, the area of China’s cold regions decreased by 49.32 × 104 km2. The findings of this study provide references for studying changes in the natural environment due to climate change, as well as for studying changes on a global scale.

Turing instability and pattern formations for reaction-diffusion systems on 2D bounded domain

<p style='text-indent:20px;'>In this article, Turing instability and the formations of spatial patterns for a general two-component reaction-diffusion system defined on 2D bounded domain, are investigated. By analyzing characteristic equation at positive constant steady states and further selecting diffusion rate <inline-formula><tex-math id="M1">\begin{document}$ d $\end{document}</tex-math></inline-formula> and diffusion ratio <inline-formula><tex-math id="M2">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> as bifurcation parameters, sufficient and necessary conditions for the occurrence of Turing instability are established, which is called the first Turing bifurcation curve. Furthermore, parameter regions in which single-mode Turing patterns arise and multiple-mode (or superposition) Turing patterns coexist when bifurcations parameters are chosen, are described. Especially, the boundary of parameter region for the emergence of single-mode Turing patterns, consists of the first and the second Turing bifurcation curves which are given in explicit formulas. Finally, by taking diffusive Schnakenberg system as an example, parameter regions for the emergence of various kinds of spatially inhomogeneous patterns with different spatial frequencies and superposition Turing patterns, are estimated theoretically and shown numerically.</p>

Species composition, spatial distribution characteristics and topographic attribution of vegetation in the water-level-fluctuating zone of the Nuozhadu Reservoir in the Lancang River Basin

澜沧江最大梯级水库——糯扎渡水库运行之后，消落带许多原有植被物种被淹消亡，造成大面积次生裸地以及严重水土流失现象.消落带植被亟待生态修复，但缺乏基本数据支撑和参考.2020年7月，基于轻型无人机支持下的3S技术，结合现场调研，采用神经网络模型、空间叠加分析、景观格局指数以及典型相关性分析等方法，提取了糯扎渡水库典型消落带植被分类图及地形数据，定量分析了研究区本土物种组成、面积、覆盖率、分布特征、景观空间格局及地形解释.结果显示，研究区消落带植被覆盖率达74.13%，涵盖18种植物，物种数量仅占蓄水前的18.9%，原生植物仅剩飞机草（Chromolaena odorata）存活，物种组成趋于简单，以一年生草本和多年生草本为主，分别占比55.56%、33.33%，菊科占据优势，苍耳（Xanthium sibiricum）、狗牙根（Cynodon dactylon）、牛筋草（Eleusine indica）和藿香蓟（Ageratum conyzoides）为主要优势物种，分别占比47.41%、29.39%、9.37%和4.56%，可作为生态修复备选物种.地形因子对消落带植被影响大小：高程>地表起伏度>水体距离>坡度>地形湿度指数>坡向.研究区优势植物均呈聚集分布，消落带中下部、上部分别以苍耳和狗牙根斑块为主导，苍耳和狗牙根在斑块优势度、连通性以及形状复杂性方面均远大于牛筋草和藿香蓟，表现出了较强的生存潜力.苍耳在地表起伏度0~1.26 m区段覆盖良好，狗牙根、牛筋草在地表起伏度0.78~2.07 m区段覆盖良好，当地表起伏度>2.07 m，植被生长困难.植被景观格局的破碎化程度、斑块形状复杂性分别与地表起伏度呈正相关、负相关，即地表起伏度越大导致植被景观格局越破碎和斑块形状越简单，进而导致种群生存力减弱.;After the operation of the Nuozhadu Reservoir, the largest cascade reservoir along the Lancang River, the original vegetation in the water-level-fluctuating zone (WLFZ) was inundated and extinguished, resulting in large areas of secondary bare ground and severe soil erosion. Ecological restoration of vegetation in the WLFZ is necessary but lacking basic data support and scientific reference. In this paper, based on 3S technology supported by light drones and combined with field research, a neural network model, spatial superposition analysis, landscape pattern index and typical correlation analysis were used to extract the vegetation classification map and topographic data of the typical WLFZ of the Nuozadu Reservoir in July 2020, and to intuitively and quantitatively analyze the native species composition, area, coverage, distribution characteristics along the terrain, landscape spatial pattern and their topographic attribution in the study area. The results showed that the vegetation coverage of the study area reached 74.13%, covering 18 species of plants, with the number of species only 18.9% of that before the construction of the reservoir. Only Chromolaena odorata (Chr) survived in the native plants. The species composition tended to be simple, with annual and perennial herbs dominating, accounting for 55.56% and 33.33% respectively, with Asteraceae as the dominant family, Xanthium sibiricum (Xan), Cynodon dactylon (Cyn), Eleusine indica (Ele) and Ageratum conyzoides (Age) were the dominant species, accounting for 47.41%, 29.39%, 9.37% and 4.56% respectively, and could be used as alternative species for restoration. The vegetation in the WLFZ was affected by topographic factors in the following order:elevation>surface fluctuation>nearest water distance>slope>topographic humidity index>slope direction. The dominant plants in the study area were all aggregated distributed, with patches of Xan and Cyn dominating the lower-middle part and upper part of the WLFZ respectively, with Xan and Cyn showing much greater patch dominance, connectivity and shape complexity than Ele and Age, showing a stronger potential for survival. Xan was well covered in the 0-1.26 m section of surface fluctuation, and Cyn and Ele were well covered in the 0.78-2.07 m section of surface fluctuation. When the surface fluctuation was >2.07 m, the vegetation growth was difficult. The degree of fragmentation of the vegetation landscape pattern and the complexity of the patch shape were positively and negatively correlated with the surface fluctuation respectively, i.e. the greater the surface fluctuation led to the more fragmented and simple shape of the vegetation landscape pattern, which in turn led to a reduction in the viability of the population.

Study on the ecological control line in the major leakage area of Baotu spring in Shandong province, eastern China

Delimiting the red line of ecologically functional space is a system innovation in the field of environmental management in China. This study proposes a method to delineate the spatial red line of ecological functions based on the strong leakage area in Jinan. The ecological control line was delineated by comprehensively considering the influence of topographic slope, lithologic characteristics, tectonic development, thickness and permeability of Quaternary strata, and vegetation coverage. And the vector analysis of these indicators was carried out in ArcGIS, the ecological control lines of the main seepage areas were initially determined by spatial superposition of vector data. In addition, the accuracy of the ecological control lines was effectively improved by vegetation cover and Quaternary stratigraphic thickness. Our results show that the major leakage areas, major leakage protection areas, and buffer areas were 299.75 km2, 114.38 km2, and 185.23 km2, respectively. The near-natural, development-construction, and new development-construction leakage areas were 221.43 km2, 60.97 km2, and 17.35 km2, respectively. This study provides support for the restoration of urban natural ecology, highlighting urban characteristics and orderly implementation of urban organic renewal, and it is of great significance to protect the regional ecology and ensure the continuous flow of Baotu Spring.

Qudits for witnessing quantum-gravity-induced entanglement of masses under decoherence

Recently a theoretical and an experimental protocol known as quantum gravity induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses each placed in a superposition of two locations. If, after eliminating all non-gravitational interactions between them, the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e. a virtual graviton. In this paper, we examine a range of different experimental set-ups, considering different geometries and the number of spatially superposed states taken, in order to determine which would generate entanglement faster. We conclude that without decoherence, and given a maximum distance $\Delta x$ between any two spatial states of a superposition, a set of two qubits placed in spatial superposition parallel to one another will outperform all other models given realistic experimental parameters. Furthermore, when a sufficiently high decoherence rate is introduced, multi-component superpositions can outperform the two-qubit set-up. This is further verified with an experimental simulation, showing that $O(10^3)$ measurements are required to reject the no entanglement hypothesis with a parallel qubits set-up without decoherence at a 99.9$\%$ confidence level. The number of measurements increases when decoherence is introduced. When the decoherence rate reaches $0.125$~Hz, 6-dimensional qudits are required as the two-qubit system entanglement cannot be witnessed anymore. However, in this case, $O(10^6)$ measurements will be required. One can group the witness operators to measure in order to reduce the number of measurements (up to ten-fold). However, this may be challenging to implement experimentally.

A new method for spatial mode shifting of stabilized optical cavities for the generation of dual-color X-rays

We propose an innovative method to shift the transversal position of the focal point of an optical cavity keeping it actively frequency stabilized. Our cavity is a 4 mirrors bow-tie cavity and the spatial shift of the resonant mode is obtained by properly rotating the two curved mirrors by piezo actuators. This method allows us to move the transversal position of the cavity focal point of 135µm in a time of 50ms, keeping the resonance condition of the cavity by means of the Pound–Drever–Hall technique. We propose to use this technique for the generation of 2-color X-rays via Inverse Compton Scattering (ICS). This technique exploits the large average power stored in the high finesse cavity by shifting the laser beam with respect to the electron beam trajectory, hence controlling the spatial superposition of the electron and photon beams in the interaction region. Arranging two cavities assembled one on top of the other, with different collision angle with the electron beam, allows the generation of X-ray bursts of different energies just by swiftly moving the two cavities, switching the two focal points onto the electron beam trajectory, thus activating in sequence two different ICS spectral lines.

Inner architectural characteristics of wave-dominated shoreface deposits and their geological implications: A case study of Devonian ‘Donghe sandstones’ in Tarim Basin, China

Wave-dominated shoreface sands are important marine clastic reservoirs, the inner spatial superposition of which causes the complex oil-water relationship in this kind of reservoir, restricting further exploitation; they develops widely in Devonian ‘Donghe sandstones’ of the Tarim Basin in China. Controlled by the genetic mode, static drilling and dynamic development data were applied to analyze these sands—focusing on three orders of architectural units namely the composite sand-bodies (5th order), single sand-body (4th order), and internal component units (3rd order). Furthermore, the identification marks and spatial distribution features of inner architectural units were investigated, and the corresponding architectural model established. Based on methods such as model fitting and control, interface identification, and analysis of well data, the single sand-body and its internal component units were identified, and the spatial superposition relationship was analyzed. In retrograding composite sand-bodies, three types of distribution patterns for the single sand-body including thick-layer refill, step migration, and continuous on-lap are present; contrarily, in prograding composite sand-bodies, the superimposed styles of the single sand-body are primarily thick-layer cumulation, step migration, and continuous overlay. The single sand-body is divided into one or more internal component units by the architectural interface of 3rd order, presenting a low-angle landward or seaward migration style. The oil-water distribution in wave-dominated shoreface reservoirs is substantially influenced by sand architecture, and architectural interfaces of different orders separate the sedimentary sand-bodies into relatively independent fluid systems, leading to differences in oil-gas production possibility among the independent layers. The wave-dominated shoreface architectural model can provide reasonable explanations for contentious factors such as the oblique oil-water interface, and production contradictions such as the mismatch between water injection and oil recovery, and resolve disagreements on well-deployment through prediction of the distribution of remaining oil, all of which have great significance for oil and gas exploration and production.

Spatial distribution of human activity intensity in Yunnan-Guizhou Plateau Wetland scenic area: A case study of Lashihai watershed in Yunnan Province, China

Human activity intensity is mostly used to quantify the degree of human influence on natural systems, with obvious spatial variability. With Lashihai watershed in Yunnan Province as an example, we used SPOT remote sensing images to update land use data, and obtained a comprehensive index of land use intensity after gridding by assigning weights to different land types, which was considered as the basic human activity intensity. The local tourism activities (horseback riding and boating) were also included. The horseback riding and boating were spatially quantified according to the location of horse farms and the abundance of horses and boats which were superimposed with the basic human activity intensity on the spatial scale of 100 m×100 m to obtain a more accurate comprehensive human activity intensity and to analyze the spatial variations. The results showed that the gridding and the kernel density analysis improved the accuracy of spatial analysis and reflected the spatial superposition and diffusion effects. In the comprehensive human activity intensity map of Lashihai watershed, the highest intensity value of water area was at the mouth of the sea, the lowest intensity value was at the center of the sea, and the overall trend of intensity gradually decreased from the surrounding to the middle. The land settlement had the highest intensity, the intensity value of the agricultural land gathering area was at the middle level, and the intensity of human activities in the forestry area of higher altitude was lower. The comprehensive human activity intensity in the water area of the Lashihai watershed varied most obviously, and differed greatly from the basic human activity intensity. Although there were many local characteristic tourism activities in Yunnan-Guizhou Plateau Wetland scenic area, but their land use types did not change. We need to take them into account when quantifying the intensity of human activities.

Multifactor-based spatio-temporal analysis of effects of urbanization and policy interventions on ecosystem service capacity: A case study of Pingshan River Catchment in Shenzhen city, China

Urbanization significantly influences the capacity of ecosystems to provide services for humans. A better understanding of the response of ecosystem service capacity (ESC) to urbanization is essential for sustainable urban planning. The purpose of this study is to analyze the spatio-temporal patterns of ESC change during rapid urbanization in the Pingshan River Catchment in Shenzhen, China. We developed a multifactor analysis approach that links urban planning decisions to the ESC by integrating policy intervention-related variables, i.e., anthropogenic pressures and the typology, size, and spatial distribution of ecosystem service suppliers. Built-up areas and transportation systems associated with urbanization were two factors determining the interference intensity of anthropogenic pressures. The main ecosystem service suppliers were ecological lands involved in urban planning, including water bodies, forest lands, and grass lands. We performed a multifactor-based spatial superposition analysis in a geographic information system to produce spatio-temporal distribution maps of the ESC. Results revealed that with urbanization in 1990–2018, the ESC experienced a fluctuating downward trend before witnessing an upward trend. Areas with moderate ESC and above reduced from 63.3 % of the catchment area to 2.9 % in 1990–2015, and then increased to 21.3 % in 2018. This pattern of ESC change was mainly attributed to the extensive urban development since 1990, together with a series of environmental protection policy initiatives formulated since 2005. In terms of spatial distribution, the areas with moderate ESC and above dramatically reduced by 66.3 % during the study period and were predominantly located within ecological control zones by 2018. Based on the current status of the ESC, our findings can be beneficial to identify and prioritize urban intervention strategies, including land conservation, restoration, enhancement, retirement, and low-impact development. The proposed approach can also be applied to ESC evaluation and sustainable urban development of other urban regions.

General Relativistic Decoherence with Applications to Dark Matter Detection.

Quantum mechanics allows for states in macroscopic superpositions, but they ordinarily undergo rapid decoherence due to interactions with their environment. A system that only interacts gravitationally, such as an arrangement of dark matter (DM), may exhibit slow decoherence. In this Letter, we compute the decoherence rate of a quantum object within general relativity, focusing on superposed metric oscillations; a rare quantum general relativistic result. For axion DM in a superposition of the field's phase, we find that DM in the MilkyWay is robust against decoherence, while a spatial superposition is not. This novel phase behavior may impact direct detection experiments.

Modeling the fire response of reactive powder concrete beams with due consideration to explosive spalling

Reactive powder concrete (RPC) is susceptible to fire-induced spalling because of its dense microstructure and lower permeability compared with normal-strength concrete and high-strength concrete, which may compromise the structural integrity and load-carrying capacity of RPC members significantly. A macroscopic finite-element model was therefore extended to track the fire behavior of RPC beams, especially fire-induced spalling. New sorption isotherms were used to identify the mass of liquid water in RPC at elevated temperatures. Furthermore, an improved spalling criterion was proposed, based on the biaxial strength theory of RPC, to judge if the spalling occurs in RPC members. Additionally, the effect of the improved and previous spalling criteria (based on the uniaxial strength theory) on the fire performance prediction of RPC beams was studied. It was found that the improved spalling criterion can provide more-accurate spalling and fire performance prediction for RPC beams since it considers the effect of both the stresses induced by pore pressure, thermal gradients and applied load and the change in concrete strength caused by the spatial stress superposition.

Thermal interactions in large irregular fields of geothermal boreholes: the method of equivalent boreholes

A new method is presented to evaluate thermal interactions between vertical geothermal boreholes. The finite line source (FLS) solution is extended to consider thermal interactions between groups of boreholes. Groups of boreholes that share similar temperatures and heat extraction rates are identified using hierarchical agglomerative clustering, and each group is represented in the model as a single equivalent borehole. Each equivalent borehole is split into segments, and temporal and spatial superposition of the FLS solution are employed to calculate the total temperature change along the length of the equivalent boreholes. The new method is shown to provide an accurate calculation of the g-function, with a mean absolute percentage error below 0.612% on the g-functions of regular borefields of up to 144 boreholes using only 3 to 5 equivalent boreholes. Calculation times are significantly reduced: the g-function of a borefield of 1024 randomly positioned boreholes is calculated in 3.65 s.

Generation of spatially unpolarized light by a Cornu depolarizer: equator polarization states as type II unpolarized light

We demonstrate the generation of spatially unpolarized light by exploiting a quartz Cornu depolarizer. Linearly polarized light impinging on the depolarizer is spatially polarization-dispersed, and the output polarization state is analyzed by a Schaefer-Collett or Berry-Gabrielse-Livingston polarimeter and a CCD camera or a photo detector, respectively. The ensemble of the observed spatially resolved normalized Stokes parameters s1(x, y), s2(x, y), s3(x, y) and the spatially resolved degree of polarization DOP(x, y) together with their counterparts spatially integrated over the beam profile show that the full beam is in fact spatially unpolarized light. The light consists of a spatial superposition of the manifold of all purely linearly polarized states encompassing completely the equator of the Poincaré sphere, thus so-called equator states. The accompanying invariance under the influence of a half-wave plate suggests that this is type II unpolarized light.

Analysis and Reduction of Phase Noise Effects in Multi-Channel Microwave Photonic Systems

Microwave photonic applications such as beamforming and ltering entail the photonic summation of optically-carried RF signals. The most commonly used components to perform these functions are ber-optic couplers, arrayed waveguide gratings and optical concentrators, whose common characteristic is to gather these optical signals on a single output before converting them into an RF signal with a photodiode. The spatial superposition of several optical elds causes photonic interference leading to the emergence of noise in the RF domain. This paper focuses on an experimental study of the impact of optical interference and phase decorrelation between delayed optical elds in an optical ber interferometer, considering two different combining technologies. When a ber coupler is employed, the full overlap of the spatial elds induces a high-level noise on the electrical signal generated after the photodiode. To solve this problem, the use of a microwave photonic summation device based on an optical power concentrator and a high-speed planar photodiode permits a strong mitigation of the optical interference. The results of the experiments presented reveal that the proposed approach can reduce phase noise effects on the resulting electrical sum signal by a factor of 40 dB.

FLAT CIRCULAR SOLENOID BETWEEN MASSIVE BIFILAR COILS. ANALYSIS OF ELECTROMAGNETIC PROCESSES

An analysis and numerical estimates of induction effects in the metal of a flat circular solenoid located between the branches of an external bifilar coil in a flat inductor system excited by unidirectional currents in the bifilar windings are presented. Such a device, the design of which was first proposed earlier by the authors of this work, is of practical interest for circuits of equipment for magnetic-pulse processing of metals. The use of the considered inductor system makes it possible to minimize the influence of induction effects on electromagnetic processes in the metal of the internal inductor. Numerical estimates are obtained for the induced currents excited in the metal of the inner circular inductor placed between the outer windings of the bifilar coil. It is shown that in the low-frequency mode of acting fields, the time dependence of the excited current is a derivative of the time dependence of the exciting current and the transverse distribution of the current in the metal of the internal inductor is a linear dependence passing through the central axis of the inductor. In the high-frequency regime of acting fields, the time dependence and the radial distribution of the excited current coincide with the corresponding analogs for the exciting current, and the transverse distribution of the induced current is characteristic of a sharp surface effect, when the induced current is displaced to the boundary surfaces of the metal. It is proved that the minimum influence of the fields of the external bifilar on the electromagnetic processes in the internal inductor should be observed in the low-frequency mode, when the spatial superposition of multidirectional induced currents adds up to the zero value of the excited electromotive force of induction. The results of the analysis based on the specific calculations performed are aimed at finding the conditions for the successful technical implementation of the proposed inductor system. The creation of workable models of the proposed inductor systems and experiments to determine the real conditions for their maximum efficiency are seen as very promising in the direction of subsequent research.

Assessment of local outburst flood risk from successive landslides: Case study of Baige landslide-dammed lake, upper Jinsha river, eastern Tibet

Two large landslides in October and November 2018 sequentially dammed the Jinsha river at Baige village, eastern Tibet, China. Subsequently, breaching of each dam induced massive outburst floods that posed a severe threat to downstream cities and infrastructure. Field investigation indicates volumes of the first and second landslide dam are about 24.5 × 106 m3 and 8.53 × 106 m3, respectively. However, the peak discharge of the flood generated from the second landslide (3.1 × 104 m3/s) was significantly larger than that from the first (1.0 × 104 m3/s). The second peak discharge would have been 5.15 × 104 m3/s if the dam breached naturally. In this study, we developed two geometry parameters: effective dam height He (elevation difference between overtopping level and river bottom) and a narrowing number distribution Nr(H) (measures the degree to which a river section is occupied by landslide materials to elevation H) which represents river section narrowing effects of successive landslides. Using numerical simulations, we show that He dominates peak discharge, and it has a linear relationship with peak discharge with slope of 1009.4 m2/s. Furthermore, the dam includes two sub-areas: a higher part (SB-1) and a lower part (SB-2). Two floods only eroded SB-2. However, breaching of SB-1 and breached SB-2 still narrowed the river. The narrowing effects of the first and second breached dam on the river channel are around 0.35 and 0.5, respectively. Spillway and landslide runup deposits increased the local flood risk by narrowing and lifting the local river section; the first landslide promoted the second landslide, which occupied the same area and forms a dam with high He value. Consequently, a more catastrophic flood could be triggered by a small subsequent landslide. Spatial superposition phenomenon of successive landslides increased the local flood risk. This research quantitatively analyzed the influence of the geometry of dam induced by successive landslides on the process of outburst floods and the risk.

Entanglement amplification between superposed detectors in flat and curved spacetimes

We consider an entanglement harvesting protocol between two Unruh-deWitt detectors in quantum superpositions of static trajectories in the static de Sitter and thermal Minkowski spacetimes. We demonstrate for the first time that the spatial superposition of each detector's path allows entanglement to be harvested from the quantum field in regimes where it would be otherwise impossible for detectors on classical trajectories. Surprisingly, for detectors on sufficiently delocalized trajectories in a thermal bath, the amount of harvested entanglement grows with the temperature of the field, violating a no-go theorem derived by Simidzija et al. [Phys. Rev. D 98, 085007]. We also discover interesting effects for mutual information harvesting, which depends sensitively on the nonlocal correlations between the superposed trajectories between the paths of the respective detectors.

Artificial aquifer recharge and pumping: transient analytical solutions for hydraulic head and impact on streamflow rate based on the spatial superposition method

The behaviour of transient groundwater mounds in response to infiltration from surface basins has been studied for decades, but some common settings still lack analytical solutions. It has been shown that applying mathematical integration to the line-sink solution developed by Hantush in the 1960s for pumping an unconfined aquifer, considering recharge over the surface of a defined area, is identical to his solution for groundwater mounding below a rectangular basin. This implies that the superposition principle can, generally, be used to directly include pumping wells, as well as aquifer boundaries, to derive a unique solution. Moreover, other line-sink solutions can be used with a spatial superposition method for addressing a variety of hydrogeological settings, provided the behaviour of the relevant partial differential equations is linear. Based on this principle and on existing line-sink solutions, several analytical solutions are proposed that are able to consider a rectangular recharging area and a pumping well in an unconfined aquifer: (1) near a stream, (2) between a stream and a no-flow boundary, with and without the influence of natural recharge, (3) near a stream that partially penetrates an aquifer and (4) for a multi-layer aquifer. For cases including streams, transient solutions of the impact on streamflow rate are also presented. The proposed analytical solutions will be of practical use for managed aquifer recharge, in particular the design of structures for artificially recharging an aquifer, possibly pumped by one or several wells.

Evaluation of landslide susceptibility based on the occurrence mechanism of landslide: a case study in Yuan' an county, China

Landslide is one of the most serious and widespread disasters in natural disasters, which seriously endangers the lives and property of residents. Based on the occurrence mechanism of landslide, this paper uses the analytic hierarchy process-comprehensive index (AHP-CI) model and takes Yuan'an County in China as an example to study and evaluate the susceptibility characteristics of landslides in this area. The geological conditions in Yuan’ an County are complex, and the landslide is extremely serious. This paper will discuss separately from the inherent factors and the inducing factors that lead to the occurrence of landslides. Combined with the geological environment conditions of Yuan' an County, 5 inherent factors, including the slope, slope structure, rock and soil characteristics, geological structure, and the lithology were selected as evaluation indexes in this evaluation. Based on the spatial superposition function of GIS, the landslide susceptibility in Yuan' an county was evaluated and zoned. And in the chapter of analysis and discussion, the influence mechanism of two induced factors of rainfall and human activities on the occurrence of landslide was discussed. Since the inherent factors could not be easily changed, but the induced factors could be controlled artificially, so according to the evaluation results, scientific prevention and control measures could be put forward for different grades of landslide prone areas in the study area. This paper studied the evaluation of landslide susceptibility based on the occurrence mechanism of landslide, which has good practicability and can provide important reference for the evaluation and prevention of landslide susceptibility in other areas.

Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions

We examine the relation between the Szekeres models and relativistic Lagrangian perturbation schemes, in particular the relativistic Zel'dovich approximation (RZA). We show that the second class of the Szekeres solutions is exactly contained within the RZA when the latter is restricted to an irrotational dust source with a flow-orthogonal foliation of spacetime. In such a case, the solution is governed by the first principal scalar invariant of the deformation field, proving a direct connection with a class of Newtonian three-dimensional solutions without symmetry. For the second class, a necessary and sufficient condition for the vanishing of cosmological backreaction on a scale of homogeneity is expressed through integral constraints. Domains with no backreaction can be smoothly matched, forming a lattice model, where exact deviations average out at a given scale of homogeneity, and the homogeneous and isotropic background is recovered as an average property of the model. Although the connection with the first class of Szekeres solutions is not straightforward, this class allows for the interpretation in terms of a spatial superposition of nonintersecting fluid lines, where each world line evolves independently and under the RZA model equations, but with different associated ``local backgrounds''. This points to the possibility of generalizing the Lagrangian perturbation schemes to structure formation models on evolving backgrounds, including global cosmological backreaction.