Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the qua...Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric is obtained.展开更多
The experimental data represented in the bibliography are theoretically analyzed to construct an adequate model for dynamics of an open nonequilibrium living system. It is shown that the viable microorganisms are capa...The experimental data represented in the bibliography are theoretically analyzed to construct an adequate model for dynamics of an open nonequilibrium living system. It is shown that the viable microorganisms are capable of forming the fractal structure, whose dimensionality is certainly non-integral. In addition, we have attempted to provide a generalized description of the properties of living and nonliving matter (in the addition to that described in work [1]). Relevant published data were used to demonstrate a fractal structure of the space in the vicinity of centrally gravitating bodies with satellites revolving around them along closed trajectories and serving as a kind of testers of the neighboring space. A local violation of its discontinuity is likely to be a necessary (yet not sufficient!) dynamic characteristic of the spatiotemporal continuum for self-organization of molecules into a living, i.e., self-replicating, system.展开更多
This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the acc...This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.展开更多
Existing orthogonal space-time block coding(OSTBC)schemes for backscatter communication systems cannot achieve a full transmission code rate when the tag is equipped with more than two antennas.In this paper,we propos...Existing orthogonal space-time block coding(OSTBC)schemes for backscatter communication systems cannot achieve a full transmission code rate when the tag is equipped with more than two antennas.In this paper,we propose a quasi-orthogonal spacetime block code(QOSTBC)that can achieve a full transmission code rate for backscatter communication systems with a four-antenna tag and then extend the scheme to support tags with 2i antennas.Specifically,we first present the system model for the backscatter system.Next,we propose the QOSTBC scheme to encode the tag signals.Then,we provide the corresponding maximum likelihood detection algorithms to recover the tag signals.Finally,simulation results are provided to demonstrate that our proposed QOSTBC scheme and the detection algorithm can achieve a better transmission code rate or symbol error rate performance for backscatter communication systems compared with benchmark schemes.展开更多
In this paper,we propose a hybrid decode-and-forward and soft information relaying(HDFSIR)strategy to mitigate error propagation in coded cooperative communications.In the HDFSIR approach,the relay operates in decode-...In this paper,we propose a hybrid decode-and-forward and soft information relaying(HDFSIR)strategy to mitigate error propagation in coded cooperative communications.In the HDFSIR approach,the relay operates in decode-and-forward(DF)mode when it successfully decodes the received message;otherwise,it switches to soft information relaying(SIR)mode.The benefits of the DF and SIR forwarding strategies are combined to achieve better performance than deploying the DF or SIR strategy alone.Closed-form expressions for the outage probability and symbol error rate(SER)are derived for coded cooperative communication with HDFSIR and energy-harvesting relays.Additionally,we introduce a novel normalized log-likelihood-ratio based soft estimation symbol(NL-SES)mapping technique,which enhances soft symbol accuracy for higher-order modulation,and propose a model characterizing the relationship between the estimated complex soft symbol and the actual high-order modulated symbol.Further-more,the hybrid DF-SIR strategy is extended to a distributed Alamouti space-time-coded cooperative network.To evaluate the~performance of the proposed HDFSIR strategy,we implement extensive Monte Carlo simulations under varying channel conditions.Results demonstrate significant improvements with the hybrid technique outperforming individual DF and SIR strategies in both conventional and distributed Alamouti space-time coded cooperative networks.Moreover,at a SER of 10^(-3),the proposed NL-SES mapping demonstrated a 3.5 dB performance gain over the conventional averaging one,highlighting its superior accuracy in estimating soft symbols for quadrature phase-shift keying modulation.展开更多
The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set(VCTS)at a minimal but safe distance.To guarantee collision avoidance,the safety distance should be calcula...The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set(VCTS)at a minimal but safe distance.To guarantee collision avoidance,the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking(EB)trajectories of two successive units during the whole EB process.In this case,the minimal safety distance is usually numerically calculated without an analytic formulation.Thus,the constrained VCTS control problem is hard to address with space-time separation,which is still a gap in the existing literature.To solve this problem,we propose a Distributed Economic Model Predictive Control(DEMPC)approach with computation efficiency and theoretical guarantee.Specifically,to alleviate the computation burden,we transform implicit safety constraints into explicitly linear ones,such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently.For theoretical analysis,sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC,employing compatibility constraints,tube techniques and terminal ingredient tuning.Moreover,we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS.Finally,experimental results demonstrate the performance and advantages of the proposed approaches.展开更多
In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary rando...In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.展开更多
Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,ca...Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.展开更多
In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time back...In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time background.The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constantΛand the topological parameterαof the geometry.The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated,utilizing two sets of rainbow functions:(i)f(χ)=■,h(χ)=1 and(ii)f(χ)=1,h(χ)=1+βХ/2.Here 0<(Х=■)≤1 with E representing the particle's energy,Ep is the Planck's energy,andβis the rainbow parameter.We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results.Afterwards,we study the quantum dynamics of quantum oscillator fields within this BML space-time,employing the Klein–Gordon oscillator.Here also,we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields.Notably,we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant.Furthermore,we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.展开更多
This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the me...This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.展开更多
As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal...As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.展开更多
Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregat...Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregate.The five combinations,in which 10%,32%,and 48%Wollastonite were added,were made for scanning using both scanning electron microscopy(SEM)and computed tomography scan technology(CT).Then,the 2D SEM pictures and the 3D pore distribution curves are obtained before and after the freezing and thawing processes,where the micro-pores in the CCM materials are shown.The fractal dimension is used to quantify the topography image in two dimensions,as well as the pore distribution in three dimensions.This method allows for the determination of both surface porosity and volume porosity,both of which show an increase in response to an escalation of freeze-thaw cycles.It is also found that the micro-damage in the concrete is of self-similarity,and in the context of the fractal dimension,the pore evolution can be quantitatively characterized across different sizes,ranging from local to global levels,before and after freezing and thawing.展开更多
Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature ...Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.展开更多
Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potentia...Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.展开更多
During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is ...During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is needed to replace the standard perturbation model of structure formation. Recently, we have been developing a model of cosmology that accounts for a large number of the observed properties of the universe. A key component of this model is that fractal structures that later regulated the creation of both matter and radiation came into existence during the initial Planck-era inflation. Initially, the vacuum was the only existence and since time, distance, and energy were uncertain, its only property, the curvature (or energy), was most likely distributed randomly. Everything that happened after the Planck era can be described by the known laws of physics so the remaining fundamental problem is to discover how such a random beginning could organize itself into the hierarchy of highly non-random self-similar structures on all length scales that are necessary to explain the existence of all cosmic structures. In this paper, we present a variation of the standard sandpile model that points to a solution. Incidental to our review of the distributions of cosmic structures, we discovered that the apparent transition from a fractal to a homogeneous distribution of structures at a distance of about 150 Mpc is a consequence of the finite size of the universe rather than a change in the underlying statistics of the distributions.展开更多
Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the...Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the self-affine,self-similarity,and iterative generation characteristics of fractal geometry,the Box-Counting Dimension method is introduced as a quantitative tool to measure the dimensions of the roof plane,facade,and spatial shape of Wuzhen Grand Theatre and Harbin Grand Theatre.The research shows that the geometric complexity of Wuzhen Grand Theater in the“fifth façade”and multi-faceted façade is significantly higher than that of Harbin Grand Theater,and its morphological design is more inclined to echo the texture of the surrounding water towns.The Harbin Grand Theater realizes the dialogue with the natural environment with simple nonlinear lines.The research proves that fractal dimension can effectively quantify the complexity of architectural form,provide a scientific basis for the form design,environmental integration,and form interpretation of performance architecture,and expand the mathematical analysis dimension of architectural form design.展开更多
To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based...To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.展开更多
Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishe...Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.展开更多
WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphol...WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphological Division and Fractal Models”,Acta Geologica Sinica-English Edition(Accepted Article):https://doi.org/10.1111/1755-6724.15094.展开更多
Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we prop...Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we propose the FractalNet-LSTM model,which combines fractal convolutional units with recurrent long short-term memory(LSTM)layers to model time series efficiently.To test the effectiveness of the model,data with complex structures and patterns,in particular,with seasonal and cyclical effects,were used.To better demonstrate the obtained results and the formed conclusions,the model performance was shown on the datasets of electricity consumption,sunspot activity,and Spotify stock price.The result showed that the proposed model outperforms traditional approaches at medium forecasting horizons and demonstrates high accuracy for data with long-term and cyclical dependencies.However,for financial data with high volatility,the model’s efficiency decreases at long forecasting horizons,indicating the need for further adaptation.The findings suggest further adaptation.The findings suggest that integrating fractal properties into neural network architecture improves the accuracy of time series forecasting and can be useful for developing more accurate and reliable forecasting systems in various industries.展开更多
文摘Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric is obtained.
文摘The experimental data represented in the bibliography are theoretically analyzed to construct an adequate model for dynamics of an open nonequilibrium living system. It is shown that the viable microorganisms are capable of forming the fractal structure, whose dimensionality is certainly non-integral. In addition, we have attempted to provide a generalized description of the properties of living and nonliving matter (in the addition to that described in work [1]). Relevant published data were used to demonstrate a fractal structure of the space in the vicinity of centrally gravitating bodies with satellites revolving around them along closed trajectories and serving as a kind of testers of the neighboring space. A local violation of its discontinuity is likely to be a necessary (yet not sufficient!) dynamic characteristic of the spatiotemporal continuum for self-organization of molecules into a living, i.e., self-replicating, system.
基金supported by the Advance Research Project of Civil Aerospace Technology(Grant No.D020304)National Nat-ural Science Foundation of China(Grant Nos.52205257 and U22B2083).
文摘This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.
基金supported by Beijing Municipal Natural Science Foundation(L222002)the Natural Science Foundation of China(U22B2004).
文摘Existing orthogonal space-time block coding(OSTBC)schemes for backscatter communication systems cannot achieve a full transmission code rate when the tag is equipped with more than two antennas.In this paper,we propose a quasi-orthogonal spacetime block code(QOSTBC)that can achieve a full transmission code rate for backscatter communication systems with a four-antenna tag and then extend the scheme to support tags with 2i antennas.Specifically,we first present the system model for the backscatter system.Next,we propose the QOSTBC scheme to encode the tag signals.Then,we provide the corresponding maximum likelihood detection algorithms to recover the tag signals.Finally,simulation results are provided to demonstrate that our proposed QOSTBC scheme and the detection algorithm can achieve a better transmission code rate or symbol error rate performance for backscatter communication systems compared with benchmark schemes.
基金funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2024-02-02160).
文摘In this paper,we propose a hybrid decode-and-forward and soft information relaying(HDFSIR)strategy to mitigate error propagation in coded cooperative communications.In the HDFSIR approach,the relay operates in decode-and-forward(DF)mode when it successfully decodes the received message;otherwise,it switches to soft information relaying(SIR)mode.The benefits of the DF and SIR forwarding strategies are combined to achieve better performance than deploying the DF or SIR strategy alone.Closed-form expressions for the outage probability and symbol error rate(SER)are derived for coded cooperative communication with HDFSIR and energy-harvesting relays.Additionally,we introduce a novel normalized log-likelihood-ratio based soft estimation symbol(NL-SES)mapping technique,which enhances soft symbol accuracy for higher-order modulation,and propose a model characterizing the relationship between the estimated complex soft symbol and the actual high-order modulated symbol.Further-more,the hybrid DF-SIR strategy is extended to a distributed Alamouti space-time-coded cooperative network.To evaluate the~performance of the proposed HDFSIR strategy,we implement extensive Monte Carlo simulations under varying channel conditions.Results demonstrate significant improvements with the hybrid technique outperforming individual DF and SIR strategies in both conventional and distributed Alamouti space-time coded cooperative networks.Moreover,at a SER of 10^(-3),the proposed NL-SES mapping demonstrated a 3.5 dB performance gain over the conventional averaging one,highlighting its superior accuracy in estimating soft symbols for quadrature phase-shift keying modulation.
基金supported by the National Natural Science Foundation of China(52372310)the State Key Laboratory of Advanced Rail Autonomous Operation(RAO2023ZZ001)+1 种基金the Fundamental Research Funds for the Central Universities(2022JBQY001)Beijing Laboratory of Urban Rail Transit.
文摘The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set(VCTS)at a minimal but safe distance.To guarantee collision avoidance,the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking(EB)trajectories of two successive units during the whole EB process.In this case,the minimal safety distance is usually numerically calculated without an analytic formulation.Thus,the constrained VCTS control problem is hard to address with space-time separation,which is still a gap in the existing literature.To solve this problem,we propose a Distributed Economic Model Predictive Control(DEMPC)approach with computation efficiency and theoretical guarantee.Specifically,to alleviate the computation burden,we transform implicit safety constraints into explicitly linear ones,such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently.For theoretical analysis,sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC,employing compatibility constraints,tube techniques and terminal ingredient tuning.Moreover,we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS.Finally,experimental results demonstrate the performance and advantages of the proposed approaches.
基金supported by the Shenzhen sustainable development project:KCXFZ 20201221173013036 and the National Natural Science Foundation of China(91746107).
文摘In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.
基金supported by the National Natural Science Foundation of China (No.61971412)。
文摘Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.
文摘In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time background.The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constantΛand the topological parameterαof the geometry.The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated,utilizing two sets of rainbow functions:(i)f(χ)=■,h(χ)=1 and(ii)f(χ)=1,h(χ)=1+βХ/2.Here 0<(Х=■)≤1 with E representing the particle's energy,Ep is the Planck's energy,andβis the rainbow parameter.We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results.Afterwards,we study the quantum dynamics of quantum oscillator fields within this BML space-time,employing the Klein–Gordon oscillator.Here also,we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields.Notably,we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant.Furthermore,we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.
文摘This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.
基金financially supported by the National Key R&D Program of China(No.2022YFE0121300)the National Natural Science Foundation of China(No.52374376)the Introduction Plan for High-end Foreign Experts(No.G2023105001L)。
文摘As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.
文摘Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregate.The five combinations,in which 10%,32%,and 48%Wollastonite were added,were made for scanning using both scanning electron microscopy(SEM)and computed tomography scan technology(CT).Then,the 2D SEM pictures and the 3D pore distribution curves are obtained before and after the freezing and thawing processes,where the micro-pores in the CCM materials are shown.The fractal dimension is used to quantify the topography image in two dimensions,as well as the pore distribution in three dimensions.This method allows for the determination of both surface porosity and volume porosity,both of which show an increase in response to an escalation of freeze-thaw cycles.It is also found that the micro-damage in the concrete is of self-similarity,and in the context of the fractal dimension,the pore evolution can be quantitatively characterized across different sizes,ranging from local to global levels,before and after freezing and thawing.
基金supported by The National Natural Science Foundation of China(Grant Nos.12272411 and 42007259).
文摘Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.
文摘Chaoshan drawnwork handkerchief design exhibits self-similarity and fractal characteristics due to their grid-based structure,overall symmetry,and the way local motifs reflect the whole pattern.To explore the potential of fractals in traditional textile design,a fractal-based generative framework was proposed for efficiently creating drawnwork patterns suitable for practical handicraft production.The research was initiated with an analysis of the structural composition of center,skeleton,and filler motifs extracted from a pattern sample library.Based on this hierarchical classification,the box-counting method was employed to calculate their respective fractal dimensions.Building on fractal art theory,generative algorithms,and studies on the application of Ultra Fractal,a Chaoshan drawnwork fractal design model was established.Using this model,51 drawnwork fractal patterns and 153 handkerchief patterns were generated.These patterns were subsequently applied in real-world production to validate the feasibility and value of fractal techniques in textile design.
文摘During the past few decades, it has become clear that the distribution, sizes, and masses of cosmic structures are best described as fractal rather than homogeneous. This means that an entirely different formalism is needed to replace the standard perturbation model of structure formation. Recently, we have been developing a model of cosmology that accounts for a large number of the observed properties of the universe. A key component of this model is that fractal structures that later regulated the creation of both matter and radiation came into existence during the initial Planck-era inflation. Initially, the vacuum was the only existence and since time, distance, and energy were uncertain, its only property, the curvature (or energy), was most likely distributed randomly. Everything that happened after the Planck era can be described by the known laws of physics so the remaining fundamental problem is to discover how such a random beginning could organize itself into the hierarchy of highly non-random self-similar structures on all length scales that are necessary to explain the existence of all cosmic structures. In this paper, we present a variation of the standard sandpile model that points to a solution. Incidental to our review of the distributions of cosmic structures, we discovered that the apparent transition from a fractal to a homogeneous distribution of structures at a distance of about 150 Mpc is a consequence of the finite size of the universe rather than a change in the underlying statistics of the distributions.
基金Jiangxi Province Intelligent Building Engineering Research Center Open Fund Project,Fractal Theory of Performing Architectural Form Design Research(Project No.:EZ202111440).
文摘Based on the fractal theory,this paper takes the form of performing architecture as the research object,and systematically discusses the application value of fractal dimension in architectural design.By expounding the self-affine,self-similarity,and iterative generation characteristics of fractal geometry,the Box-Counting Dimension method is introduced as a quantitative tool to measure the dimensions of the roof plane,facade,and spatial shape of Wuzhen Grand Theatre and Harbin Grand Theatre.The research shows that the geometric complexity of Wuzhen Grand Theater in the“fifth façade”and multi-faceted façade is significantly higher than that of Harbin Grand Theater,and its morphological design is more inclined to echo the texture of the surrounding water towns.The Harbin Grand Theater realizes the dialogue with the natural environment with simple nonlinear lines.The research proves that fractal dimension can effectively quantify the complexity of architectural form,provide a scientific basis for the form design,environmental integration,and form interpretation of performance architecture,and expand the mathematical analysis dimension of architectural form design.
基金funded by the National Key Research and Development ProgramFund for Young Scientists(No.2021YFC2900400)+5 种基金the National Natural Science Foundation of China(No.52304123)Fundamental Research Funds for the Central Universities(No.2024CDJXY025)Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(No.CSTB2024TIAD-CYKJCXX0016)Postdoctoral Research Foundation of China(No.2023M730412)Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(No.GZB20230914)Chongqing Outstanding Youth Science Foundation Program(No.CSTB2023NSCQ-JQX0027)。
文摘To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.
基金funded by the National Key R&D Program of China,China(Grant No.2023YFB4005500)National Natural Science Foundation of China,China(Grant Nos.52379113 and 52379114).
文摘Gas-liquid two-phase flow in fractal porous media is pivotal for engineering applications,yet it remains challenging to be accurately characterized due to complex microstructure-flow interactions.This study establishes a pore-scale numerical framework integratingMonte Carlo-generated fractal porousmedia with Volume of Fluid(VOF)simulations to unravel the coupling among pore distribution characterized by fractal dimension(Df),flow dynamics,and displacement efficiency.A pore-scale model based on the computed tomography(CT)microstructure of Berea sandstone is established,and the simulation results are compared with experimental data.Good agreement is found in phase distribution,breakthrough behavior,and flow path morphology,confirming the reliability of the numerical simulation method.Ten fractal porous media models with Df ranging from 1.25~1.7 were constructed using a Monte-Carlo approach.The gas-liquid two-phase flow dynamics was characterized using the VOF solver across gas injection rates of 0.05-5m/s,inwhich the time-resolved two-phase distribution patternswere systematically recorded.The results reveal that smaller fractal dimensions(Df=1.25~1.45)accelerate fingering breakthrough(peak velocity is 1.73 m/s at Df=1.45)due to a bimodal pore size distribution dominated by narrow channels.Increasing Df amplifies vorticity generation by about 3 times(eddy viscosity is 0.033 Pa⋅s at Df=1.7)through reduced interfacial curvature,while tortuosity-driven pressure differentials transition from sharp increases(0.4~6.3 Pa at Df=1.25~1.3)to inertial plateaus(4.8 Pa at Df=1.7).A nonlinear increase in equilibrium gas volume fraction(fav=0.692 at Df=1.7)emerges from residual gas saturation and turbulence-enhanced dispersion.This behavior is further modulated by flow velocity,with fav peaking at 0.72 under capillary-dominated conditions(0.05 m/s),but decreasing to 0.65 in the inertial regime(0.5 m/s).The work quantitatively links fractal topology to multiphase flow regimes,demonstrating the critical role of Df in governing preferential pathways,energy dissipation,and phase distribution.
文摘WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphological Division and Fractal Models”,Acta Geologica Sinica-English Edition(Accepted Article):https://doi.org/10.1111/1755-6724.15094.
文摘Time series forecasting is important in the fields of finance,energy,and meteorology,but traditional methods often fail to cope with the complex nonlinear and nonstationary processes of real data.In this paper,we propose the FractalNet-LSTM model,which combines fractal convolutional units with recurrent long short-term memory(LSTM)layers to model time series efficiently.To test the effectiveness of the model,data with complex structures and patterns,in particular,with seasonal and cyclical effects,were used.To better demonstrate the obtained results and the formed conclusions,the model performance was shown on the datasets of electricity consumption,sunspot activity,and Spotify stock price.The result showed that the proposed model outperforms traditional approaches at medium forecasting horizons and demonstrates high accuracy for data with long-term and cyclical dependencies.However,for financial data with high volatility,the model’s efficiency decreases at long forecasting horizons,indicating the need for further adaptation.The findings suggest further adaptation.The findings suggest that integrating fractal properties into neural network architecture improves the accuracy of time series forecasting and can be useful for developing more accurate and reliable forecasting systems in various industries.
