A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

Fractal analysis of major faults and fractal dimension of lineaments in the Indo-Gangetic Plain on a regional scale

The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.

An Exploration of the Three Dimensions and Epochal Strengths of Building a Human Community With a Shared Future

The idea of a human community with a shared future was proposed by the Communist Party of China(CPC)Central Committee with Comrade Xi Jinping at its core for the future development of human beings to face up to the most important question in today's world:“What is happening to the world and what should we do?”It profoundly answers the question of the world,history,and the times.The theory of a human community with a shared future is an innovative theory with a multidimensional formation logic that guides humanity toward continually seeking common interests and values.This paper dives into the profound motivations behind building a human community with a shared future from historical,cultural,and practical dimensions and analyzes its epochal value from both domestic and international perspectives.This not only helps exert China's role in the international community,contributing Chinese strength to the construction of a peaceful,stable,and prosperous human society,but also enhances the influence of the idea of a human community with a shared future in the international community,accelerating the building of a human community with a shared future that considers the legitimate concerns of all countries,and aiding in solving the crises facing the world.

DOA estimation of high-dimensional signals based on Krylov subspace and weighted l_(1)-norm

With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direction of arrival(DOA)estimation due to the computational complexity of algorithms.Traditional subspace algorithms require estimation of the covariance matrix,which has high computational complexity and is prone to producing spurious peaks.In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements,this paper proposes a DOA estimation method based on Krylov subspace and weighted l_(1)-norm.The method uses the multistage Wiener filter(MSWF)iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace,further uses the measurement matrix to reduce the dimensionality of the signal subspace observation,constructs a weighted matrix,and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted l_(1)-norm to solve the target DOA.Simulation results show that the proposed method has high resolution under large array conditions,effectively suppresses spurious peaks,reduces computational complexity,and has good robustness for low signal to noise ratio(SNR)environment.

Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

The Historical Position and Value Dimensions of Human Rights Civilization

Human beings are the mainstay and the ultimate goal of civilization.The history of human civilization is a continuous struggle to realize the respect,liberation,protection,and development of humanity.Human rights are an achievement of humanity and a symbol of progress,and the human rights civilization is an important component of human civilization.Understanding and interpreting human rights from the perspective of human rights civilization means that human rights are not only a concept or an idea but also a grand historical and long-term social practice.Up to now,the development of human rights civilization has roughly experienced four awakening eras:initialization,revolution,popularization,and globalization.In terms of its value dimensions,it has the characteristics of progressiveness,diversity,commonality,inclusiveness,indivisibility,openness,and so on.The historical position of human rights civilization and the development of its value dimensions have shown to the world that human rights are the common wealth of humanity,and human rights belong to all mankind;human rights are historical,concrete,and developmental;the concept of human rights is constantly evolving,and its connotations and categories are constantly expanding;achieving the free and well-rounded development of every person is the highest value realm of human rights civilization.The Chinese modernization endows Chinese civilization with modern strength and opens up new horizons for human rights civilization.The new pattern of human rights civilization to be created by Chinese modernization not only possesses the common characteristics of human rights civilization but also enjoys Chinese characteristics based on its own national conditions,enriching and developing the diversity of human rights civilization for all mankind.

The Global Attractor and Its Dimension Estimation of Generalized Kolmogorov-Petrovlkii-Piskunov Equation

In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.

Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines

Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.

Measurement Uncertainty Analysis of the Rotary-scan Method for the Measurable Dimension of Cylindrical Workpieces

The measurement uncertainty analysis is carried out to investigate the measurable dimensions of cylindrical workpieces by the rotary-scan method in this paper.Due to the difficult alignment of the workpiece with a diameter of less than 3 mm by the rotary scan method,the measurement uncertainty of the cylindrical workpiece with a diameter of 3 mm and length of 50 mm which is measured by a roundness measuring machine,is evaluated according to GUM(Guide to the Expression of Uncertainty in Measurement)as an example.Since the uncertainty caused by the eccentricity of the measured workpiece is different with the dimension changing,the measurement uncertainty of cylindrical workpieces with other dimensions can be evaluated the same as the diameter of 3 mm but with different eccentricity.Measurement uncertainty caused by different eccentricities concerning the dimension of the measured cylindrical workpiece is set to simulate the evaluations.Compared to the target value of the measurement uncertainty of 0.1μm,the measurable dimensions of the cylindrical workpiece can be obtained.Experiments and analysis are presented to quantitatively evaluate the reliability of the rotary-scan method for the roundness measurement of cylindrical workpieces.

Further Analysis of Machine Tool Dimensional Accuracy and Thermal Stability under Varying Floor Temperature

Machining is as old as humanity, and changes in temperature in both the machine’s internal and external environments can be of great concern as they affect the machine’s thermal stability and, thus, the machine’s dimensional accuracy. This paper is a continuation of our earlier work, which aimed to analyze the effect of the internal temperature of a machine tool as the machine is put into operation and vary the external temperature, the machine floor temperature. Some experiments are carried out under controlled conditions to study how machine tool components get heated up and how this heating up affects the machine’s accuracy due to thermally induced deviations. Additionally, another angle is added by varying the machine floor temperature. The parameters mentioned above are explored in line with the overall thermal stability of the machine tool and its dimensional accuracy. A Robodrill CNC machine tool is used. The CNC was first soaked with thermal energy by gradually raising the machine floor temperature to a certain level before putting the machine in operation. The machine was monitored, and analytical methods were deplored to evaluate thermal stability. Secondly, the machine was run idle for some time under raised floor temperature before it was put into operation. Data was also collected and analyzed. It is observed that machine thermal stability can be achieved in several ways depending on how the above parameters are joggled. This paper, in conclusion, reinforces the idea of machine tool warm-up process in conjunction with a carefully analyzed and established machine floor temperature variation for the approximation of the machine tool’s thermally stability to map the long-time behavior of the machine tool.

3-Dimensional Kinematic Comparison of Arm Movements between an Individual with NGLY1 Deficiency and a Neurotypical Individual

NGLY1 Deficiency is an ultra-rare autosomal recessively inherited disorder. Characteristic symptoms include among others, developmental delays, movement disorders, liver function abnormalities, seizures, and problems with tear formation. Movements are hyperkinetic and may include dysmetric, choreo-athetoid, myoclonic and dystonic movement elements. To date, there have been no quantitative reports describing arm movements of individuals with NGLY1 Deficiency. This report provides quantitative information about a series of arm movements performed by an individual with NGLY1 Deficiency and an aged-matched neurotypical participant. Three categories of arm movements were tested: 1) open ended reaches without specific end point targets;2) goal-directed reaches that included grasping an object;3) picking up small objects from a table placed in front of the participants. Arm movement kinematics were obtained with a camera-based motion analysis system and “initiation” and “maintenance” phases were identified for each movement. The combination of the two phases was labeled as a “complete” movement. Three-dimensional analysis techniques were used to quantify the movements and included hand trajectory pathlength, joint motion area, as well as hand trajectory and joint jerk cost. These techniques were required to fully characterize the movements because the NGLY1 individual was unable to perform movements only in the primary plane of progression instead producing motion across all three planes of movement. The individual with NGLY1 Deficiency was unable to pick up objects from a table or effectively complete movements requiring crossing the midline. The successfully completed movements were analyzed using the above techniques and the results of the two participants were compared statistically. Almost all comparisons revealed significant differences between the two participants, with a notable exception of the 3D initiation area as a percentage of the complete movement. The statistical tests of these measures revealed no significant differences between the two participants, possibly suggesting a common underlying motor control strategy. The 3D techniques used in this report effectively characterized arm movements of an individual with NGLY1 deficiency and can be used to provide information to evaluate the effectiveness of genetic, pharmacological, or physical rehabilitation therapies.

Suppression of stimulated Raman scattering by angularly incoherent light, towards a laser system of incoherence in all dimensions of time, space, and angle

Laser–plasma instability(LPI)is one of the main obstacles to achieving predictable and reproducible fusion at high gain through laser-driven inertial confinement fusion(ICF).In this paper,for the first time,we show analytically and confirm with three-dimensional particle-incell simulations that angular incoherence provides suppression of the instability growth rate that is additional to and much stronger than that provided by the well-known temporal and spatial incoherence usually used in ICF studies.For the model used in our calculations,the maximum field ratio between the stimulated Raman scattering and the driving pulses drops from 0.2 for a Laguerre–Gaussian pulse with a single nonzero topological charge to 0.05 for a super light spring with an angular momentum spread and random relative phases.In particular,angular incoherence does not introduce extra undesirable hot electrons.This provides a novel method for suppressing LPI by using light with an angular momentum spread and paves the way towards a low-LPI laser system for inertial fusion energy with a super light spring of incoherence in all dimensions of time,space,and angle,and may open the door to the use of longer-wavelength lasers for inertial fusion energy.

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

Volume fractal dimension of soil particles and relationships with soil physical-chemical properties and plant species diversity in an alpine grassland under different disturbance degrees

Fractal geometry is an important method in soil science,and many studies have used fractal theory to examine soil properties and the relationships with other eco-environmental factors.However,there have been few studies examining soil particle volume fractal dimension in alpine grasslands.To study the volume fractal dimension of soil particles （D） and its relationships with soil salt,soil nutrient and plant species diversity,we conducted an experiment on an alpine grassland under different disturbance degrees：non-disturbance （N0）,light disturbance （L）,moderate disturbance （M） and heavy disturbance （H）.The results showed that （1） Ds varied from 2.573 to 2.635 among the different disturbance degrees and increased with increasing degrees of disturbance.（2） Shannon-Wiener diversity index,Pielou＇s evenness index and Margalef richness index reached their highest values at the M degree,indicating that moderate disturbance is beneficial to the increase of plant species diversity.（3） In the L and M degrees,there was a significant positive correlation between D and clay content and a significant negative correlation between D and soil organic matter （SOM）.In the H degree,D was significantly and positively correlated with total salt （TS）.The results suggested that to a certain extent,D can be used to characterize the uniformity of soil texture in addition to soil fertility characteristics.（4） For the L degree,there was a significant negative correlation between D and the Shannon-Wiener diversity index; while for the M degree,there was a significant negative correlation between D and Pielou＇s evenness index.

Fractal dimension of coal particles and their CH_4 adsorption

We describe the fractal analysis of three differently sized coal samples(0.350-0.833 mm,0.245-0.350 mm,and 0.198-0.245 mm).The influence of fractal dimension on CH 4 adsorption capacity is investigated.The physical parameters of the samples were determined via the Brunauer-Emmett-Teller(BET) theory.A CH 4 adsorption study over the pressures range from 0 to 5 MPa was carried out with a new volumetric measurement system.The CH 4 adsorption was measured using the differently sized coal.Two fractal dimensions,D 1 and D 2 were determined over the pressure ranges from 0 to 0.5 MPa and from 0.5 to 1 MPa,using the Frenkel-Halsey-Hill(FHH) method.We conclude that the two fractal dimensions correlate with the CH 4 adsorption capacity of the coal:increasing CH 4 adsorption capacity occurs with a corresponding increase in fractal dimension.Furthermore,D 1 and D 2 are positively correlated with surface area,pore volume,and samples size.The size distribution of the samples has fractal characteristics.

ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS

In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].

A New Dynamics Analysis Model for Five-Axis Machining of Curved Surface Based on Dimension Reduction and Mapping

The equipment used in various fields contains an increasing number of parts with curved surfaces of increasing size.Five-axis computer numerical control(CNC)milling is the main parts machining method,while dynamics analysis has always been a research hotspot.The cutting conditions determined by the cutter axis,tool path,and workpiece geometry are complex and changeable,which has made dynamics research a major challenge.For this reason,this paper introduces the innovative idea of applying dimension reduction and mapping to the five-axis machining of curved surfaces,and proposes an efficient dynamics analysis model.To simplify the research object,the cutter position points along the tool path were discretized into inclined plane five-axis machining.The cutter dip angle and feed deflection angle were used to define the spatial position relationship in five-axis machining.These were then taken as the new base variables to construct an abstract two-dimensional space and establish the mapping relationship between the cutter position point and space point sets to further simplify the dimensions of the research object.Based on the in-cut cutting edge solved by the space limitation method,the dynamics of the inclined plane five-axis machining unit were studied,and the results were uniformly stored in the abstract space to produce a database.Finally,the prediction of the milling force and vibration state along the tool path became a data extraction process that significantly improved efficiency.Two experiments were also conducted which proved the accuracy and efficiency of the proposed dynamics analysis model.This study has great potential for the online synchronization of intelligent machining of large surfaces.

Effect of particle gradation on pore structure and seepage law of solution in weathered crust elution-deposited rare earth ores

Both CT and Avizo software were used to explore the effect of particle gradation on the evolution characteristics of pore structure and seepage paths in weathered crust elution-deposited rare earth ores during leaching.The results showed that the pore areas in four kinds of ore samples before leaching were mainly concentrated in 10^(4)–10^(7)μm^(2),whose pore quantities accounted for 96.89%,94.94%,90.48%,and 89.45%,respectively,while the corresponding pore volume only accounted for 30.74%,14.55%,7.58%,and 2.84%of the total pore volume.With the decrease of fractal dimension,the average pore throat length increased,but pore throat quantities,the average pore throat radius and coordination number decreased.Compared with that before leaching,the change degree of pore structure during leaching increased with the fractal dimension decreasing.For example,the reduction rate of the average coordination number of ore samples was 14.36%,21.30%,28.00%,and 32.90%,respectively.Seepage simulation results indicated that seepage paths were uniformly distributed before leaching while the streamline density and seepage velocity increased with the fractal dimension decreasing.Besides,the phenomenon of the streamline interruption gradually reduced during leaching while preferential seepage got more obvious with the decrease of the fractal dimension.

Bounds on Fractional-Based Metric Dimension of Petersen Networks

The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.