The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈...The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.展开更多
Shock tunnels are indispensable facilities for hypersonic aerodynamic experimentation.Within these systems,the diaphragm plays a pivotal role,as its rupture process critically influences shock wave generation quality,...Shock tunnels are indispensable facilities for hypersonic aerodynamic experimentation.Within these systems,the diaphragm plays a pivotal role,as its rupture process critically influences shock wave generation quality,experimental repeatability,and facility reliability.A thorough understanding of diaphragm rupture dynamics is therefore essential for optimizing shock tunnel design,improving experimental accuracy,and ensuring operational safety.To address the complex challenge of fully coupled multiphysics analysis in high-pressure-ratio shock tunnels,this study introduces a high-fidelity,three-dimensional,fully coupled Fluid-Structure Interaction(FSI)simulation framework.This framework seamlessly integrates the Dual Conservation Element and Solution Element(Dual-CESE)method,the Immersed Boundary Method(IBM),and the JohnsonCook(J-C)material constitutive and failure model.The combined approach enables synchronized simulation and analysis of the entire diaphragm rupture sequence—including pre-deformation,crack initiation and propagation,and fully developed petaling deformation—alongside the formation and evolution of the associated supersonic flow field.The simulation results show strong agreement with experimental observations,with the post-rupture geometric morphology accurately replicated and a shock wave velocity deviation of only 2.55%from experimental measurements.The study uncovers the dynamic failure mechanisms,revealing that nonlinear pressure loading initiates cracking within the diaphragm.It further elucidates how the nonlinearly coupled interactions between petaling dynamics and fracture morphology directly impact shock wave formation and evolution.This computational framework provides a novel and robust methodology for advancing shock tunnel design and conducting comprehensive reliability assessments.展开更多
Using multi-source reanalysis data,this study examines the relationship between the tropical Pacific-Atlantic SST Dipole Mode(TPA-DM)and summer precipitation in North China(NCSP)on the interannual timescale during the...Using multi-source reanalysis data,this study examines the relationship between the tropical Pacific-Atlantic SST Dipole Mode(TPA-DM)and summer precipitation in North China(NCSP)on the interannual timescale during the period of 1979-2022.The results show that the TPA-DM,the dominant pattern of interannual variability in the tropical Pacific and Atlantic regions,exhibits a significant negative correlation with NCSP.The positive phase of TPA-DM induces subsidence over the Maritime Continent through a zonal circulation pattern,which initiates a Pacific-Japan-like wave train along the East Asian coast.The circulation anomalies lead to moisture deficits and convergence subsidence over North China,leading to below-normal rainfall.Further analysis reveals that cooler SST in the Southern Tropical Atlantic facilitates the persistence of the TPA-DM by stimulating the anomalous Walker circulation associated with wind-evaporation-SST-convection feedback.展开更多
The modeling and dynamical analysis of discrete chaotic systems is a vital research field,and various chaotic maps have been developed using mathematical and control-theoretic approaches.However,physical circuit desig...The modeling and dynamical analysis of discrete chaotic systems is a vital research field,and various chaotic maps have been developed using mathematical and control-theoretic approaches.However,physical circuit design of mathematically defined discrete chaotic systems and the computation of their energy functions remain challenging and open problems.In this study,a two-dimensional(2D)chaotic map is constructed using an open-loop modulation coupling method,and its dynamical characteristics are analyzed using bifurcation diagrams.Lyapunov exponents(LEs)and spectral entropy(SE)complexity are also inspected under different parameter configurations.Furthermore,the proposed chaotic map is expressed using two distinct physical memristive circuits:one is composed of a magnetic flux-controlled memristor,a nonlinear resistor,and a capacitor;the other utilizes a charge-controlled memristor,a nonlinear resistor,and an inductor.Moreover,two energy functions are derived from the two memristor-coupled circuits for the proposed chaotic map.The results demonstrate that the mathematical model of the discrete chaotic system can be effectively expressed through these two nonlinear circuits.Our study offers a theoretical foundation and viable methodology for the physical circuit representation of discrete chaotic systems and determination of their energy functions.展开更多
Rock damage significantly affects coupled thermo-hydro-mechanical(THM)behavior in deep geothermal exploitation through changing thermal and hydrological properties of rocks.For this,a thermo-hydro-mechanical-damage(TH...Rock damage significantly affects coupled thermo-hydro-mechanical(THM)behavior in deep geothermal exploitation through changing thermal and hydrological properties of rocks.For this,a thermo-hydro-mechanical-damage(THMD)coupled model was developed to describe the coupling between rock damage and mechanical,fluid flow and heat transfer fields.The model considers rock heterogeneity,and incorporates the Mohr-Coulomb failure criterion and the maximum tensile stress criterion to evaluate shear and tensile damage.This numerical modeling methodology was first verified against analytical solutions and experimental results,and was then used to simulate the THMD coupling behavior in deep geothermal exploitation.A coupled numerical model was set up to simulate the geothermal fluids extraction and re-injection process in a reservoir at 1 km depth over a 7-year period.Rock damage was found to accelerate the propagation of cold fronts away from the injection well,and have a distinct effect on the performance of geothermal exploitation.When the rock damage was considered,the field injectivity increases by 8.4 times,the range of cooled regions increases by 18.6 times,and the vertical deformation changes by 1.2 times after 7 years of geothermal operations,compared to the scenario where it was not considered.Parametric studies have suggested that thermal contraction dominates the rock damage evolution,and that thermal-induced rock damage only occurs at a sufficiently large temperature difference between fluids injected and the reservoir.This work underscores the importance of accurately accounting for the damage effect on reservoir response during fluid injection activities that cause significant cooling of reservoir rocks.展开更多
Vacancy defects,as fundamental disruptions in metallic lattices,play an important role in shaping the mechanical and electronic properties of aluminum crystals.However,the influence of vacancy position under coupled t...Vacancy defects,as fundamental disruptions in metallic lattices,play an important role in shaping the mechanical and electronic properties of aluminum crystals.However,the influence of vacancy position under coupled thermomechanical fields remains insufficiently understood.In this study,transmission and scanning electron microscopy were employed to observe dislocation structures and grain boundary heterogeneities in processed aluminum alloys,suggesting stress concentrations and microstructural inhomogeneities associated with vacancy accumulation.To complement these observations,first-principles calculations and molecular dynamics simulations were conducted for seven single-vacancy configurations in face-centered cubic aluminum.The stress response,total energy,density of states(DOS),and differential charge density were examined under varying compressive strain(ε=0–0.1)and temperature(0–600 K).The results indicate that face-centered vacancies tend to reduce mechanical strength and perturb electronic states near the Fermi level,whereas corner and edge vacancies appear to have weaker effects.Elevated temperatures may partially restore electronic uniformity through thermal excitation.Overall,these findings suggest that vacancy position exerts a critical but position-dependent influence on coupled structure-property relationships,offering theoretical insights and preliminary experimental support for defect-engineered aluminum alloy design.展开更多
Improving plasma uniformity is a critical issue in the development of large-area radio-frequency(RF)inductively coupled plasma(ICP)sources.In this work,the effects of coil structure and electromagnetic shielding on th...Improving plasma uniformity is a critical issue in the development of large-area radio-frequency(RF)inductively coupled plasma(ICP)sources.In this work,the effects of coil structure and electromagnetic shielding on the spatial distribution and uniformity of the plasma are systematically investigated using a three-dimensional fluid model.The model integrates plasma and electromagnetic field modules to simulate the discharge characteristics of a large-area RF ICP source with dimensions of 100 cm×50 cm.The results reveal that the electron density distribution varies significantly with the coil structure.For the rotating and translating coil structures,the electron density is high at off-axis positions and low at the center.In contrast,the mirror coil structure exhibits a significantly higher electron density at the chamber center,resulting in a high-center and low-edge density distribution.Among the three configurations,the rotating coil structure provides the best plasma uniformity.The incorporation of electromagnetic shielding further improves plasma uniformity,particularly for the mirror coil structure.For the rotating and translating coil structures,the electron density exhibits a saddle-shaped distribution regardless of electromagnetic shielding.However,introducing electromagnetic shielding into the mirror coil structure reduces the electron density at the chamber center and decreases the non-uniformity degree by 18.4%.Overall,the mirror coil structure with electromagnetic shielding achieves the highest uniformity,with an exceptional plasma uniformity of 94%.This work offers valuable insights for the design of large-area ICP sources in advanced plasma processing systems.展开更多
To reveal the influence of coupled effects of dry-wet cycling and precompression stress(CEDWCPS)on the damage evolution of limestone with horizontal fissure(LHF),a series of degradation and uniaxial compression tests ...To reveal the influence of coupled effects of dry-wet cycling and precompression stress(CEDWCPS)on the damage evolution of limestone with horizontal fissure(LHF),a series of degradation and uniaxial compression tests were conducted,and a corresponding piecewise damage constitutive model(PDCM)was established.We found that both dry-wet cycling and precompression stress deteriorate the physical properties,alter the microscopic characteristics,and reduce the mechanical properties of the LHF.These degradations are particularly pronounced under the CEDWCPS,although the magnitude of these changes gradually diminishes with the progression of dry-wet cycling.Meanwhile,they also reduce the deformation degree,prolong the micropore compaction stage,shorten the unstable crack propagation stage,lower the frequency and intensity of AE events,decrease the high-amplitude and high-frequency AE signals,enlarge crack scales,and shorten the crack initiation time.Among the changes of these indicators,the dry-wet cycling plays a dominant role.The crack types of LHF under the CEDWCPS(LHFCEDWCPS)are predominantly tensile cracks,supplemented by shear cracks.The failure mode can be defined as tensileshear composite failure.Finally,the established PDCM effectively captures the nonlinear deformation of micropore and the linear deformation of the matrix in LHFCEDWCPS,with all corresponding R^(2) consistently exceeding 0.97.展开更多
To explore the distribution law of the temperature field in the motor pump and the influence of the fanshaped DC channel with spoiler in the pump housing on its heat dissipation performance.This study takes the arc-ge...To explore the distribution law of the temperature field in the motor pump and the influence of the fanshaped DC channel with spoiler in the pump housing on its heat dissipation performance.This study takes the arc-gear type hydraulicmotor pump as the research object.In COMSOL,a coupled heat transfer simulationmodel of themotor pump’s fluid-solid coupling is established,and the internal temperature field characteristics are analyzed.To improve the heat dissipation effect of the motor pump,it is proposed to arrange spoiler in the fan-shaped DC channel of the pump housing to enhance heat dissipation.Three types of spoilers,namely,wing-shaped,inclined rectangle-shaped,and wave-shaped,are designed.The simulation results show that when the motor pump operates under rated conditions,due to the poor heat dissipation environment inside the motor pump,the high-temperature areas of the motor pump are concentrated in the rotor and permanent magnet parts.After arranging the spoiler,the turbulent kinetic energy and vorticity in the fan-shaped DC channel of the pump housing are significantly enhanced.All three spoiler structures can reduce the maximum temperature of each component of the motor.According to the comprehensive performance evaluation criterion(PEC),the inclined rectangle-shaped structure has the best comprehensive heat transfer performance(PEC=1.114),while the wave-shaped structure has higher heat transfer efficiency but greater pressure loss.The wing-shaped structure has relatively limited enhancement effect on heat dissipation.This study systematically quantifies the influence of different spoiler structures on heat dissipation performance and flowresistance characteristics,providing a solution for enhancing the heat dissipation of the motor pump.展开更多
Hypersonic morphing vehicle(HMV)can reconfigure aerodynamic geometries in real time,adapting to diverse needs like multi-mission profiles and wide-speed-range flight,spanwise morphing and sweep angle variation are rep...Hypersonic morphing vehicle(HMV)can reconfigure aerodynamic geometries in real time,adapting to diverse needs like multi-mission profiles and wide-speed-range flight,spanwise morphing and sweep angle variation are representative large-scale wing reconfiguration modes.To meet the HMV's need for an increased lift and a lift to drag ratio during hypersonic maneuverability and cruise or reentry equilibrium glide,this paper proposes an innovative single-DOF coupled morphing-wing system.We then systematically analyze its open-loop kinematics and closed-loop connectivity constraints,and the proposed system integrates three functional modules:the preset locking/release mechanism,the coupled morphing-wing mechanism,and the integrated wing locking with active stiffness control mechanism.Experimental validation confirms stable,continuous morphing under simulated aerodynamic loads.The experimental results indicate:(i)SMA actuators exhibit response times ranging from 18 s to 160 s,providing sufficient force output for wing unlocking;(ii)The integrated wing locking with active stiffness control mechanism effectively secures wing positions while eliminating airframe clearance via SMA actuation,improving the first-order natural frequency by more than 17%;(iii)The distributed aerodynamic loading system enables precise multi-stage follow-up loading during morphing,with the coupled morphing wing maintaining stable,continuous operation under 0-3500 N normal loads and 110-140 N axial force.The proposed single-DOF coupled morphing mechanism not only simplifies and improves structural efficiency but also demonstrates superior performance in locking control,stiffness enhancement,and aerodynamic responsiveness.This establishes a foundational framework for the design of future intelligent morphing configurations and the implementation of flight control systems.展开更多
The dual challenges of critical speed prediction inaccuracies and ambiguous vibration behaviors are present in high-speed flexible rotors,particularly in free turbine rotors in turboshaft engine systems.The study begi...The dual challenges of critical speed prediction inaccuracies and ambiguous vibration behaviors are present in high-speed flexible rotors,particularly in free turbine rotors in turboshaft engine systems.The study begins with an examination of the rotor-bearing bidirectional coupling mechanism,with a primary focus on the nonlinear characteristics of the bearing.An investigation is carried out on the mechanical modeling methodologies for four-point contact ball bearings(FPCBBs)and cylindrical roller bearings(CRBs).To address the issue of excessive computational time in traditional bearing calculation methods,the sled dog optimization(SDO)algorithm is substituted for the conventional Newton-Raphson method.A rotor-bearing coupling dynamics model is developed by the finite element and lumped mass methods,with experimental validation achieved through a simulator test rig.The effects of three internal bearing parameters in FPCBBs(arching width and raceway groove curvature coefficient)and CRBs(initial radial clearance)on the critical speed characteristics and vibrational behavior of rotorbearing coupled systems are examined.The numerical simulation results show some interesting conclusions.展开更多
In response to the demand for seismic-resilient structures,various innovative solutions have emerged to reduce local damage and residual deformations,facilitating repair operations in the aftermath of high-intensity e...In response to the demand for seismic-resilient structures,various innovative solutions have emerged to reduce local damage and residual deformations,facilitating repair operations in the aftermath of high-intensity earth-quakes.This paper examines the seismic performance of a steel-concrete hybrid wall system equipped with a selfcentering solution to mitigate earthquake-induced residual deformations.The considered hybrid system includes a Reinforced Concrete(RC)shear wall with two steel side columns connected by coupling steel beams.In this study,a novel type of coupling beams featuring a friction-damped self-centering system is implemented.The system is referred to as Self-Centering Hybrid Single-Pier Coupled Wall(SC-SP-HCW)and aims to minimize damage and residual deformations after earthquakes,which in turn facilitates repairs and enhances seismic resilience.Unlike conventional self-centering coupling beams with post-tensioned tendons,the self-centering configuration in this system does not rely on a gap-opening mechanism at the wall-beam connection interface,eliminating frame expansion effects.The proposed self-centering devices can also be implemented as preassembled links,which facilitates installation and reduces uncertainties associated with the on-site posttensioning procedure.The seismic performance of SC-SP-HCWs is investigated through nonlinear static and incremental dynamic analyses on case study SC-SP-HCWs designed as the lateral load-resisting systems of an eight-story building.The seismic response of the case study SC-SP-HCWs is investigated,considering both local and global engineering demand parameters(EDPs).The results demonstrate the ability of the SC-SP-HCWs to significantly reduce earthquake-induced residual deformations without exacerbating damage to structural ele-ments typically observed in conventional coupled walls.展开更多
This paper prepared a novel as-cast W-Zr-Ti metallic ESM using high-frequency vacuum induction melting technique.The above ESM performs a typical elastic-brittle material feature and strain rate strengthening behavior...This paper prepared a novel as-cast W-Zr-Ti metallic ESM using high-frequency vacuum induction melting technique.The above ESM performs a typical elastic-brittle material feature and strain rate strengthening behavior.The specimens exhibit violent chemical reaction during the fracture process under the impact loading,and the size distribution of their residual debris follows Rosin-Rammler model.The dynamic fracture toughness is obtained by the fitting of debris length scale,approximately 1.87 MPa·m~(1/2).Microstructure observation on residual debris indicates that the failure process is determined by primary crack propagation under quasi-static compression,while it is affected by multiple cracks propagation in both particle and matrix in the case of dynamic impact.Impact test demonstrates that the novel energetic fragment performs brilliant penetration and combustion effect behind the front target,leading to the effective ignition of fuel tank.For the brittleness of as-cast W-ZrTi ESM,further study conducted bond-based peridynamic(BB-PD)C++computational code to simulate its fracture behavior during penetration.The BB-PD method successfully captured the fracture process and debris cloud formation of the energetic fragment.This paper explores a novel as-cast metallic ESM,and provides an available numerical avenue to the simulation of brittle energetic fragment.展开更多
G protein-coupled receptor 37(GPR37)is an orphan receptor predominantly expressed in the brain,particularly in oligodendrocytes and certain types of neurons.Notably,it has been shown that the N-terminal domain of GPR3...G protein-coupled receptor 37(GPR37)is an orphan receptor predominantly expressed in the brain,particularly in oligodendrocytes and certain types of neurons.Notably,it has been shown that the N-terminal domain of GPR37 undergoes proteolysis under normal physiological conditions,resulting in the formation of cleaved receptor forms and the release of its ectodomain(ecto-GPR37)into the extracellular milieu(Mattila et al.,2021).Importantly,ecto-GPR37 density is increased in cerebrospinal fluid(CSF)of patients suffering from sporadic Parkinson’s disease(PD),together with an abnormal GPR37 processing in post-mortem PD substantia nigra(Moratóet al.,2021;Figure 1A).展开更多
In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutio...In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation(CEWE) and the space-time fractional coupled modified equal width wave equation(CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels.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,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are c...In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are considered in terms of radial and non-radial basis functions.The time-dependent variable in the first radial scheme is directly considered as the normal space variables to formulate an"isotropic"space-time radial basis function.The second non-radial scheme considered relationship between time-dependent and spacedependent variables.Under such circumstance,we can get a one-step space-time meshless scheme.The numerical findings demonstrate that the proposed meshless schemes are precise,user-friendly,and effective in solving the coupled Burgers'equations.展开更多
In order to obtain space-time coupling relationship of anchor-cable to improve supporting effect for deep coal mine rock roadway, FLAC3D was used to investigate into mechanical characteristics of the roadway whose cro...In order to obtain space-time coupling relationship of anchor-cable to improve supporting effect for deep coal mine rock roadway, FLAC3D was used to investigate into mechanical characteristics of the roadway whose crosssection shape was vertical wall and semi-circular arch when the roadway was supported by bolts and metal mesh. The results show that the extent of stress concentrations, the range failure zone, and the deformation at the roof center and two spandrels of roadway are greater than those at other positions, except at the floor. The reasonable positions of anchor-cable supporting are the roof center and two spandrels of roadway. The anchor-cable should be installed at good time with bolts supporting after roadway driving be- cause it can improve the stress states of deep surrounding rock around the roadway and control the roadway deformation effec- tively. The engineering practice has proven that the sustained deformation of deep surrounding rocks is effectively controlled when the anchor-cable supporting is adopted at reasonable positions of the roadway at good time.展开更多
The complexity of coupled risks,which refer to the compounded effects of interacting uncertainties across multiple interdependent objectives,is inherent to cities functioning as dynamic,interdependent systems.A disrup...The complexity of coupled risks,which refer to the compounded effects of interacting uncertainties across multiple interdependent objectives,is inherent to cities functioning as dynamic,interdependent systems.A disruption in one domain ripples across various urban systems,often with unforeseen consequences.Central to this complexity are people,whose behaviors,needs,and vulnerabilities shape risk evolution and response effectiveness.Realizing cities as complex systems centered on human needs and behaviors is essential to understanding the complexities of coupled urban risks.This paper adopts a complex systems perspective to examine the intricacies of coupled urban risks,emphasizing the critical role of human decisions and behavior in shaping these dynamics.We focus on two key dimensions:cascading hazards in urban environments and cascading failures across interdependent exposed systems in cities.Existing risk assessment models often fail to capture the complexity of these processes,particularly when factoring in human decision-making.To tackle these challenges,we advocate for a standardized taxonomy of cascading hazards,urban components,and their interactions.At its core is a people-centric perspective,emphasizing the bidirectional interactions between people and the systems that serve them.Building on this foundation,we argue the need for an integrated,people-centric risk assessment framework that evaluates event impacts in relation to the hierarchical needs of people and incorporates their preparedness and response capacities.By leveraging real-time data,advanced simulations,and innovative validation methods,this framework aims to enhance the accuracy of coupled urban risk modeling.To effectively manage coupled urban risks,cities can draw from proven strategies in real complex systems.However,given the escalating uncertainties and complexities associated with climate change,prioritizing people-centric strategies is crucial.This approach will empower cities to build resilience not only against known hazards but also against evolving and unforeseen challenges in an increasingly uncertain world.展开更多
A coupled thermal-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams is presented.Heat exchange between the cold fluid and the hot rock is considered,and the thermal contribution t...A coupled thermal-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams is presented.Heat exchange between the cold fluid and the hot rock is considered,and the thermal contribution terms between the cold fluid and the hot rock are derived.Heat transfer obeys Fourier's law,and porosity is used to relate the thermodynamic parameters of the fracture and matrix domains.The net pressure difference between the fracture and the matrix is neglected,and thus the fluid flow is modeled by the unified fluid-governing equations.The evolution equations of porosity and Biot's coefficient during hydraulic fracturing are derived from their definitions.The effect of coal cleats is considered and modeled by Voronoi polygons,and this approach is shown to have high accuracy.The accuracy of the proposed model is verified by two sets of fracturing experiments in multilayer coal seams.Subsequently,the differences in fracture morphology,fluid pressure response,and fluid pressure distribution between direct fracturing of coal seams and indirect fracturing of shale interlayers are explored,and the effects of the cluster number and cluster spacing on fracture morphology for multi-cluster fracturing are also examined.The numerical results show that the proposed model is expected to be a powerful tool for the fracturing design and optimization of deep coalbed methane.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605003 and 11547231
文摘The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.
基金supported by the National Key R&D Program of China(No.2021YFC3100700)。
文摘Shock tunnels are indispensable facilities for hypersonic aerodynamic experimentation.Within these systems,the diaphragm plays a pivotal role,as its rupture process critically influences shock wave generation quality,experimental repeatability,and facility reliability.A thorough understanding of diaphragm rupture dynamics is therefore essential for optimizing shock tunnel design,improving experimental accuracy,and ensuring operational safety.To address the complex challenge of fully coupled multiphysics analysis in high-pressure-ratio shock tunnels,this study introduces a high-fidelity,three-dimensional,fully coupled Fluid-Structure Interaction(FSI)simulation framework.This framework seamlessly integrates the Dual Conservation Element and Solution Element(Dual-CESE)method,the Immersed Boundary Method(IBM),and the JohnsonCook(J-C)material constitutive and failure model.The combined approach enables synchronized simulation and analysis of the entire diaphragm rupture sequence—including pre-deformation,crack initiation and propagation,and fully developed petaling deformation—alongside the formation and evolution of the associated supersonic flow field.The simulation results show strong agreement with experimental observations,with the post-rupture geometric morphology accurately replicated and a shock wave velocity deviation of only 2.55%from experimental measurements.The study uncovers the dynamic failure mechanisms,revealing that nonlinear pressure loading initiates cracking within the diaphragm.It further elucidates how the nonlinearly coupled interactions between petaling dynamics and fracture morphology directly impact shock wave formation and evolution.This computational framework provides a novel and robust methodology for advancing shock tunnel design and conducting comprehensive reliability assessments.
基金jointly supported by the Second Tibetan Plateau Scientific Expedition and Research Program[grant number-ber 2019QZKK0103]the National Natural Science Foundation of China[grant number 42293294]the China Meteorological Admin-istration Climate Change Special Program[grant number QBZ202303]。
文摘Using multi-source reanalysis data,this study examines the relationship between the tropical Pacific-Atlantic SST Dipole Mode(TPA-DM)and summer precipitation in North China(NCSP)on the interannual timescale during the period of 1979-2022.The results show that the TPA-DM,the dominant pattern of interannual variability in the tropical Pacific and Atlantic regions,exhibits a significant negative correlation with NCSP.The positive phase of TPA-DM induces subsidence over the Maritime Continent through a zonal circulation pattern,which initiates a Pacific-Japan-like wave train along the East Asian coast.The circulation anomalies lead to moisture deficits and convergence subsidence over North China,leading to below-normal rainfall.Further analysis reveals that cooler SST in the Southern Tropical Atlantic facilitates the persistence of the TPA-DM by stimulating the anomalous Walker circulation associated with wind-evaporation-SST-convection feedback.
基金supported by the National Natural Science Foundation of China(No.62301416).
文摘The modeling and dynamical analysis of discrete chaotic systems is a vital research field,and various chaotic maps have been developed using mathematical and control-theoretic approaches.However,physical circuit design of mathematically defined discrete chaotic systems and the computation of their energy functions remain challenging and open problems.In this study,a two-dimensional(2D)chaotic map is constructed using an open-loop modulation coupling method,and its dynamical characteristics are analyzed using bifurcation diagrams.Lyapunov exponents(LEs)and spectral entropy(SE)complexity are also inspected under different parameter configurations.Furthermore,the proposed chaotic map is expressed using two distinct physical memristive circuits:one is composed of a magnetic flux-controlled memristor,a nonlinear resistor,and a capacitor;the other utilizes a charge-controlled memristor,a nonlinear resistor,and an inductor.Moreover,two energy functions are derived from the two memristor-coupled circuits for the proposed chaotic map.The results demonstrate that the mathematical model of the discrete chaotic system can be effectively expressed through these two nonlinear circuits.Our study offers a theoretical foundation and viable methodology for the physical circuit representation of discrete chaotic systems and determination of their energy functions.
基金funded by the Major National Science and Technology Project for Deep Earth of China(Grant No.2024ZD1003805)the National Natural Science Foundation of China(Grant Nos.52311530070 and 52004015).
文摘Rock damage significantly affects coupled thermo-hydro-mechanical(THM)behavior in deep geothermal exploitation through changing thermal and hydrological properties of rocks.For this,a thermo-hydro-mechanical-damage(THMD)coupled model was developed to describe the coupling between rock damage and mechanical,fluid flow and heat transfer fields.The model considers rock heterogeneity,and incorporates the Mohr-Coulomb failure criterion and the maximum tensile stress criterion to evaluate shear and tensile damage.This numerical modeling methodology was first verified against analytical solutions and experimental results,and was then used to simulate the THMD coupling behavior in deep geothermal exploitation.A coupled numerical model was set up to simulate the geothermal fluids extraction and re-injection process in a reservoir at 1 km depth over a 7-year period.Rock damage was found to accelerate the propagation of cold fronts away from the injection well,and have a distinct effect on the performance of geothermal exploitation.When the rock damage was considered,the field injectivity increases by 8.4 times,the range of cooled regions increases by 18.6 times,and the vertical deformation changes by 1.2 times after 7 years of geothermal operations,compared to the scenario where it was not considered.Parametric studies have suggested that thermal contraction dominates the rock damage evolution,and that thermal-induced rock damage only occurs at a sufficiently large temperature difference between fluids injected and the reservoir.This work underscores the importance of accurately accounting for the damage effect on reservoir response during fluid injection activities that cause significant cooling of reservoir rocks.
基金supported by the Research Project on Strengthening the Construction of an Important Ecological Security Barrier in Northern China by Higher Education Institutions in the Inner Mongolia Autonomous Region(STAQZX202313)the Inner Mongolia Autonomous Region Education Science‘14th Five-Year Plan’2024 Annual Research Project(NGJGH2024635).
文摘Vacancy defects,as fundamental disruptions in metallic lattices,play an important role in shaping the mechanical and electronic properties of aluminum crystals.However,the influence of vacancy position under coupled thermomechanical fields remains insufficiently understood.In this study,transmission and scanning electron microscopy were employed to observe dislocation structures and grain boundary heterogeneities in processed aluminum alloys,suggesting stress concentrations and microstructural inhomogeneities associated with vacancy accumulation.To complement these observations,first-principles calculations and molecular dynamics simulations were conducted for seven single-vacancy configurations in face-centered cubic aluminum.The stress response,total energy,density of states(DOS),and differential charge density were examined under varying compressive strain(ε=0–0.1)and temperature(0–600 K).The results indicate that face-centered vacancies tend to reduce mechanical strength and perturb electronic states near the Fermi level,whereas corner and edge vacancies appear to have weaker effects.Elevated temperatures may partially restore electronic uniformity through thermal excitation.Overall,these findings suggest that vacancy position exerts a critical but position-dependent influence on coupled structure-property relationships,offering theoretical insights and preliminary experimental support for defect-engineered aluminum alloy design.
基金supported by the National Natural Science Foundation of China(Grant Nos.12075049 and 11935005)。
文摘Improving plasma uniformity is a critical issue in the development of large-area radio-frequency(RF)inductively coupled plasma(ICP)sources.In this work,the effects of coil structure and electromagnetic shielding on the spatial distribution and uniformity of the plasma are systematically investigated using a three-dimensional fluid model.The model integrates plasma and electromagnetic field modules to simulate the discharge characteristics of a large-area RF ICP source with dimensions of 100 cm×50 cm.The results reveal that the electron density distribution varies significantly with the coil structure.For the rotating and translating coil structures,the electron density is high at off-axis positions and low at the center.In contrast,the mirror coil structure exhibits a significantly higher electron density at the chamber center,resulting in a high-center and low-edge density distribution.Among the three configurations,the rotating coil structure provides the best plasma uniformity.The incorporation of electromagnetic shielding further improves plasma uniformity,particularly for the mirror coil structure.For the rotating and translating coil structures,the electron density exhibits a saddle-shaped distribution regardless of electromagnetic shielding.However,introducing electromagnetic shielding into the mirror coil structure reduces the electron density at the chamber center and decreases the non-uniformity degree by 18.4%.Overall,the mirror coil structure with electromagnetic shielding achieves the highest uniformity,with an exceptional plasma uniformity of 94%.This work offers valuable insights for the design of large-area ICP sources in advanced plasma processing systems.
基金supported by the Yunnan Province Science and Technology Plan Project(No.202403AA080001-4)the Key Research and Development Project of Guangxi,China(No.guikeAB24010144)the National Key Research and Development Project of China(Nos.2021YFB3901402 and 2018YFC1504802)。
文摘To reveal the influence of coupled effects of dry-wet cycling and precompression stress(CEDWCPS)on the damage evolution of limestone with horizontal fissure(LHF),a series of degradation and uniaxial compression tests were conducted,and a corresponding piecewise damage constitutive model(PDCM)was established.We found that both dry-wet cycling and precompression stress deteriorate the physical properties,alter the microscopic characteristics,and reduce the mechanical properties of the LHF.These degradations are particularly pronounced under the CEDWCPS,although the magnitude of these changes gradually diminishes with the progression of dry-wet cycling.Meanwhile,they also reduce the deformation degree,prolong the micropore compaction stage,shorten the unstable crack propagation stage,lower the frequency and intensity of AE events,decrease the high-amplitude and high-frequency AE signals,enlarge crack scales,and shorten the crack initiation time.Among the changes of these indicators,the dry-wet cycling plays a dominant role.The crack types of LHF under the CEDWCPS(LHFCEDWCPS)are predominantly tensile cracks,supplemented by shear cracks.The failure mode can be defined as tensileshear composite failure.Finally,the established PDCM effectively captures the nonlinear deformation of micropore and the linear deformation of the matrix in LHFCEDWCPS,with all corresponding R^(2) consistently exceeding 0.97.
基金supported by the Henan Provincial Key Research and Development Special Project(251111220200)Natural Science Foundation of Henan Province Project(252300420446).
文摘To explore the distribution law of the temperature field in the motor pump and the influence of the fanshaped DC channel with spoiler in the pump housing on its heat dissipation performance.This study takes the arc-gear type hydraulicmotor pump as the research object.In COMSOL,a coupled heat transfer simulationmodel of themotor pump’s fluid-solid coupling is established,and the internal temperature field characteristics are analyzed.To improve the heat dissipation effect of the motor pump,it is proposed to arrange spoiler in the fan-shaped DC channel of the pump housing to enhance heat dissipation.Three types of spoilers,namely,wing-shaped,inclined rectangle-shaped,and wave-shaped,are designed.The simulation results show that when the motor pump operates under rated conditions,due to the poor heat dissipation environment inside the motor pump,the high-temperature areas of the motor pump are concentrated in the rotor and permanent magnet parts.After arranging the spoiler,the turbulent kinetic energy and vorticity in the fan-shaped DC channel of the pump housing are significantly enhanced.All three spoiler structures can reduce the maximum temperature of each component of the motor.According to the comprehensive performance evaluation criterion(PEC),the inclined rectangle-shaped structure has the best comprehensive heat transfer performance(PEC=1.114),while the wave-shaped structure has higher heat transfer efficiency but greater pressure loss.The wing-shaped structure has relatively limited enhancement effect on heat dissipation.This study systematically quantifies the influence of different spoiler structures on heat dissipation performance and flowresistance characteristics,providing a solution for enhancing the heat dissipation of the motor pump.
基金supported by the National Natural Science Foundation of China(Grant No.52405257)the China Postdoctoral Science Foundation(Grant No.2024M764201).
文摘Hypersonic morphing vehicle(HMV)can reconfigure aerodynamic geometries in real time,adapting to diverse needs like multi-mission profiles and wide-speed-range flight,spanwise morphing and sweep angle variation are representative large-scale wing reconfiguration modes.To meet the HMV's need for an increased lift and a lift to drag ratio during hypersonic maneuverability and cruise or reentry equilibrium glide,this paper proposes an innovative single-DOF coupled morphing-wing system.We then systematically analyze its open-loop kinematics and closed-loop connectivity constraints,and the proposed system integrates three functional modules:the preset locking/release mechanism,the coupled morphing-wing mechanism,and the integrated wing locking with active stiffness control mechanism.Experimental validation confirms stable,continuous morphing under simulated aerodynamic loads.The experimental results indicate:(i)SMA actuators exhibit response times ranging from 18 s to 160 s,providing sufficient force output for wing unlocking;(ii)The integrated wing locking with active stiffness control mechanism effectively secures wing positions while eliminating airframe clearance via SMA actuation,improving the first-order natural frequency by more than 17%;(iii)The distributed aerodynamic loading system enables precise multi-stage follow-up loading during morphing,with the coupled morphing wing maintaining stable,continuous operation under 0-3500 N normal loads and 110-140 N axial force.The proposed single-DOF coupled morphing mechanism not only simplifies and improves structural efficiency but also demonstrates superior performance in locking control,stiffness enhancement,and aerodynamic responsiveness.This establishes a foundational framework for the design of future intelligent morphing configurations and the implementation of flight control systems.
文摘The dual challenges of critical speed prediction inaccuracies and ambiguous vibration behaviors are present in high-speed flexible rotors,particularly in free turbine rotors in turboshaft engine systems.The study begins with an examination of the rotor-bearing bidirectional coupling mechanism,with a primary focus on the nonlinear characteristics of the bearing.An investigation is carried out on the mechanical modeling methodologies for four-point contact ball bearings(FPCBBs)and cylindrical roller bearings(CRBs).To address the issue of excessive computational time in traditional bearing calculation methods,the sled dog optimization(SDO)algorithm is substituted for the conventional Newton-Raphson method.A rotor-bearing coupling dynamics model is developed by the finite element and lumped mass methods,with experimental validation achieved through a simulator test rig.The effects of three internal bearing parameters in FPCBBs(arching width and raceway groove curvature coefficient)and CRBs(initial radial clearance)on the critical speed characteristics and vibrational behavior of rotorbearing coupled systems are examined.The numerical simulation results show some interesting conclusions.
基金supported by the European Union’s Horizon 2020 research and innovation program under grant agreement No.101027745(Marie Sklodowska-Curie Research Grant Scheme H2020-MSCA-IF-2020:Self-Centering Earthquake-Resilient Hybrid Steel-Concrete Shear Walls with Rocking Beams-SC-HYBWalls)the support from the Royal Society-Interna-tional Exchange programme under the grant agreement IES\R3\213175.
文摘In response to the demand for seismic-resilient structures,various innovative solutions have emerged to reduce local damage and residual deformations,facilitating repair operations in the aftermath of high-intensity earth-quakes.This paper examines the seismic performance of a steel-concrete hybrid wall system equipped with a selfcentering solution to mitigate earthquake-induced residual deformations.The considered hybrid system includes a Reinforced Concrete(RC)shear wall with two steel side columns connected by coupling steel beams.In this study,a novel type of coupling beams featuring a friction-damped self-centering system is implemented.The system is referred to as Self-Centering Hybrid Single-Pier Coupled Wall(SC-SP-HCW)and aims to minimize damage and residual deformations after earthquakes,which in turn facilitates repairs and enhances seismic resilience.Unlike conventional self-centering coupling beams with post-tensioned tendons,the self-centering configuration in this system does not rely on a gap-opening mechanism at the wall-beam connection interface,eliminating frame expansion effects.The proposed self-centering devices can also be implemented as preassembled links,which facilitates installation and reduces uncertainties associated with the on-site posttensioning procedure.The seismic performance of SC-SP-HCWs is investigated through nonlinear static and incremental dynamic analyses on case study SC-SP-HCWs designed as the lateral load-resisting systems of an eight-story building.The seismic response of the case study SC-SP-HCWs is investigated,considering both local and global engineering demand parameters(EDPs).The results demonstrate the ability of the SC-SP-HCWs to significantly reduce earthquake-induced residual deformations without exacerbating damage to structural ele-ments typically observed in conventional coupled walls.
文摘This paper prepared a novel as-cast W-Zr-Ti metallic ESM using high-frequency vacuum induction melting technique.The above ESM performs a typical elastic-brittle material feature and strain rate strengthening behavior.The specimens exhibit violent chemical reaction during the fracture process under the impact loading,and the size distribution of their residual debris follows Rosin-Rammler model.The dynamic fracture toughness is obtained by the fitting of debris length scale,approximately 1.87 MPa·m~(1/2).Microstructure observation on residual debris indicates that the failure process is determined by primary crack propagation under quasi-static compression,while it is affected by multiple cracks propagation in both particle and matrix in the case of dynamic impact.Impact test demonstrates that the novel energetic fragment performs brilliant penetration and combustion effect behind the front target,leading to the effective ignition of fuel tank.For the brittleness of as-cast W-ZrTi ESM,further study conducted bond-based peridynamic(BB-PD)C++computational code to simulate its fracture behavior during penetration.The BB-PD method successfully captured the fracture process and debris cloud formation of the energetic fragment.This paper explores a novel as-cast metallic ESM,and provides an available numerical avenue to the simulation of brittle energetic fragment.
基金FEDER/Ministerio de Ciencia,Innovacióny Universidades-Agencia Estatal de Investigación(PID2023-147425OB-I00 to FC)Agència de Gestiód’Ajuts Universitaris i de Recerca(AGAUR)-Generalitat de Catalunya(2021 SGR 00698 to FC).
文摘G protein-coupled receptor 37(GPR37)is an orphan receptor predominantly expressed in the brain,particularly in oligodendrocytes and certain types of neurons.Notably,it has been shown that the N-terminal domain of GPR37 undergoes proteolysis under normal physiological conditions,resulting in the formation of cleaved receptor forms and the release of its ectodomain(ecto-GPR37)into the extracellular milieu(Mattila et al.,2021).Importantly,ecto-GPR37 density is increased in cerebrospinal fluid(CSF)of patients suffering from sporadic Parkinson’s disease(PD),together with an abnormal GPR37 processing in post-mortem PD substantia nigra(Moratóet al.,2021;Figure 1A).
文摘In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation(CEWE) and the space-time fractional coupled modified equal width wave equation(CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels.
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the Science and Technology Research Project of Henan Province (242102231052)the Key Scientific Research Plan of Colleges and Universities in Henan Province (23B140006)the Natural Science Foundation of Jiangxi Province (20224BAB201018)。
文摘In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are considered in terms of radial and non-radial basis functions.The time-dependent variable in the first radial scheme is directly considered as the normal space variables to formulate an"isotropic"space-time radial basis function.The second non-radial scheme considered relationship between time-dependent and spacedependent variables.Under such circumstance,we can get a one-step space-time meshless scheme.The numerical findings demonstrate that the proposed meshless schemes are precise,user-friendly,and effective in solving the coupled Burgers'equations.
基金Supported by the Science and Technological Fund of Anhui Province for Outstanding Youth （1108085J02）, the National Natural Science Foundation of Anhui Province （K J2010A090）
文摘In order to obtain space-time coupling relationship of anchor-cable to improve supporting effect for deep coal mine rock roadway, FLAC3D was used to investigate into mechanical characteristics of the roadway whose crosssection shape was vertical wall and semi-circular arch when the roadway was supported by bolts and metal mesh. The results show that the extent of stress concentrations, the range failure zone, and the deformation at the roof center and two spandrels of roadway are greater than those at other positions, except at the floor. The reasonable positions of anchor-cable supporting are the roof center and two spandrels of roadway. The anchor-cable should be installed at good time with bolts supporting after roadway driving be- cause it can improve the stress states of deep surrounding rock around the roadway and control the roadway deformation effec- tively. The engineering practice has proven that the sustained deformation of deep surrounding rocks is effectively controlled when the anchor-cable supporting is adopted at reasonable positions of the roadway at good time.
基金jointly supported by the National Natural Science Foundation of China(71821001,72371109,72071088,72074089,and 51938004)Strategic Study Project of Chinese Academy of Engineering(2022-JB-02)Project of Interdisciplinary Research Support Program in Huazhong University of Science and Technology(2023-32)。
文摘The complexity of coupled risks,which refer to the compounded effects of interacting uncertainties across multiple interdependent objectives,is inherent to cities functioning as dynamic,interdependent systems.A disruption in one domain ripples across various urban systems,often with unforeseen consequences.Central to this complexity are people,whose behaviors,needs,and vulnerabilities shape risk evolution and response effectiveness.Realizing cities as complex systems centered on human needs and behaviors is essential to understanding the complexities of coupled urban risks.This paper adopts a complex systems perspective to examine the intricacies of coupled urban risks,emphasizing the critical role of human decisions and behavior in shaping these dynamics.We focus on two key dimensions:cascading hazards in urban environments and cascading failures across interdependent exposed systems in cities.Existing risk assessment models often fail to capture the complexity of these processes,particularly when factoring in human decision-making.To tackle these challenges,we advocate for a standardized taxonomy of cascading hazards,urban components,and their interactions.At its core is a people-centric perspective,emphasizing the bidirectional interactions between people and the systems that serve them.Building on this foundation,we argue the need for an integrated,people-centric risk assessment framework that evaluates event impacts in relation to the hierarchical needs of people and incorporates their preparedness and response capacities.By leveraging real-time data,advanced simulations,and innovative validation methods,this framework aims to enhance the accuracy of coupled urban risk modeling.To effectively manage coupled urban risks,cities can draw from proven strategies in real complex systems.However,given the escalating uncertainties and complexities associated with climate change,prioritizing people-centric strategies is crucial.This approach will empower cities to build resilience not only against known hazards but also against evolving and unforeseen challenges in an increasingly uncertain world.
基金Project supported by the National Natural Science Foundation of China(No.42202314)。
文摘A coupled thermal-hydro-mechanical cohesive phase-field model for hydraulic fracturing in deep coal seams is presented.Heat exchange between the cold fluid and the hot rock is considered,and the thermal contribution terms between the cold fluid and the hot rock are derived.Heat transfer obeys Fourier's law,and porosity is used to relate the thermodynamic parameters of the fracture and matrix domains.The net pressure difference between the fracture and the matrix is neglected,and thus the fluid flow is modeled by the unified fluid-governing equations.The evolution equations of porosity and Biot's coefficient during hydraulic fracturing are derived from their definitions.The effect of coal cleats is considered and modeled by Voronoi polygons,and this approach is shown to have high accuracy.The accuracy of the proposed model is verified by two sets of fracturing experiments in multilayer coal seams.Subsequently,the differences in fracture morphology,fluid pressure response,and fluid pressure distribution between direct fracturing of coal seams and indirect fracturing of shale interlayers are explored,and the effects of the cluster number and cluster spacing on fracture morphology for multi-cluster fracturing are also examined.The numerical results show that the proposed model is expected to be a powerful tool for the fracturing design and optimization of deep coalbed methane.
