Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The a...The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.展开更多
A paired basin study in the upper Santa Fe River watershed following forest thinning and prescribed burns successfully measured water budget components in a treated and an untreated (control) basin. The paired basin s...A paired basin study in the upper Santa Fe River watershed following forest thinning and prescribed burns successfully measured water budget components in a treated and an untreated (control) basin. The paired basin study was established to investigate questions that have arisen regarding changes in water yield from forest treatments. Precipitation, stream flow, soil moisture, and chloride concentrations in precipitation and stream flow were measured to quantify the water budget components. The results from eleven years of data collection and analysis have a high degree of confidence with respect to measuring the water budget components based on the mass balance of water and chloride. The differences in the geologic structure and topography between the two paired basins appeared to impact the water budgets more than the forest treatments, except during periods when winter precipitation and snowmelt represented a significant component of inflow. Although this paired basin study was not able to portray a simple relationship between forest thinning and water yield, the chloride concentration methodology used to estimate evapotranspiration (ET) was successful. These detailed observations of chloride deposition and transport characteristics may be relevant for other researchers working in forested basins with substantial ET. ET rates were estimated by examining the cycle of chloride entering and exiting each basin over six integration periods. ET was estimated to be about 90% to 94% of precipitation in the treated basin and 77% to 86% in the control basin. The higher ET in the treated basin both before and after forest treatments may be due to the much greater area of west-facing hillslopes in the treated basin, which receive warm afternoon sun, and the greater area of rock cover in the control basin. Variation in the chloride concentration of collected precipitation samples from different sites indicates that horizontal precipitation of chloride in the tree canopy is an important consideration when using the chloride mass balance approach to calculate water budget components.展开更多
Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the d...Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the deformation properties of complex fractured rock mass.It comprehends both the advantages of the discrete fracture network model and the equivalent continuum model to capture the features of discontinuities explicitly while reducing computational intensity.The complex fracture network is stochastically split into a number of subfracture networks according to the domain,length or angle.An analytical solution is derived to infer theoretically the relationship between the elastic moduli of the original complex fractured rock mass and the split subfractured rock masses by introducing a correction term based on the deformation superposition principle.Numerical simulations are conducted to determine the elastic moduli of split subfractured rock masses using universal distinct element code(UDEC),while the elastic modulus of the original model is estimated based on the currently proposed analytical relationship.The results show that the estimation accuracy with the current domainbased splitting model is far superior compared to those with the other two splitting models.Thus,the estimation method of elastic modulus of complex fractured rock mass based on domain splitting mode of fracture network is identified as the multi-domain equivalent method proposed in this paper.The reliability of this method is evaluated,and its high computational efficiency is demonstrated through exemplification with regard to different geometric configurations for stochastically artificial discrete fracture network.The proposed multi-domain equivalent method constructs the theoretical framework except for the regression analysis hypothesis compared to the density-reduced model equivalent method.展开更多
Glacier response patterns at the catchment scale are highly heterogeneous and defined by a complex interplay of various dynamics and surface factors.Previous studies have explained heterogeneous responses in qualitati...Glacier response patterns at the catchment scale are highly heterogeneous and defined by a complex interplay of various dynamics and surface factors.Previous studies have explained heterogeneous responses in qualitative ways but quantitative assessment is lacking yet where an intrazone homogeneous climate assumption can be valid.Hence,in the current study,the reason for heterogeneous mass balance has been explained in quantitative methods using a multiple linear regression model in the Sikkim Himalayan region.At first,the topographical parameters are selected from previously published studies,then the most significant topographical and geomorphological parameters are selected with backward stepwise subset selection methods.Finally,the contributions of selected parameters are calculated by least square methods.The results show that,the magnitude of mass balance lies between-0.003±0.24 to-1.029±0.24 m.w.e.a^(-1) between 2000 and 2020 in the Sikkim Himalaya region.Also,the study shows that,out of the terminus type of the glacier,glacier area,debris cover,ice-mixed debris,slope,aspect,mean elevation,and snout elevation of the glaciers,only the terminus type and mean elevation of the glacier are significantly altering the glacier mass balance in the Sikkim Himalayan region.Mathematically,the mass loss is approximately 0.40 m.w.e.a^(-1) higher in the lake-terminating glaciers compared to the land-terminating glaciers in the same elevation zone.On the other hand,a thousand meters mean elevation drop is associated with 0.179 m.w.e.a-1of mass loss despite the terminus type of the glaciers.In the current study,the model using the terminus type of the glaciers and the mean elevation of the glaciers explains 76% of fluctuation of mass balance in the Sikkim Himalayan region.展开更多
The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to ...The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.展开更多
In order to develop a anchoring operation simulation system and improve safety during anchoring operations,a relatively accurate mathematical model of anchoring operations needs to be established.In this paper,the str...In order to develop a anchoring operation simulation system and improve safety during anchoring operations,a relatively accurate mathematical model of anchoring operations needs to be established.In this paper,the stress condition of anchor chain under environmental and subsea geological conditions is further studied and the stress condition of anchor chain is analyzed based on the previous research.In this paper,a quasi-static model based on catenary method is used as the basis of dynamic analysis,and the dynamic model of anchor chain is established based on the concentrated mass method,which fully considers the influence of anchor chain weight,hydrodynamic force,ocean current and interaction with the seabed.The fourth-order Runge Kutta method was used to solve the model numerically,and a calculation procedure was developed.The accuracy of the model was verified by comparing the calculated results with the experimental results,indicating that the constructed anchor chain dynamics model has a high accuracy.展开更多
In order to identify the day and night pollution sources of PM10 in ambient air in Longyan City,the authors analyzed the elemental composition of respirable particulate matters in the day and night ambient air samples...In order to identify the day and night pollution sources of PM10 in ambient air in Longyan City,the authors analyzed the elemental composition of respirable particulate matters in the day and night ambient air samples and various pollution sources which were collected in January 2010 in Longyan with inductivity coupled plasma-mass spectrometry(ICP-MS).Then chemical mass balance(CMB) model and factor analysis(FA) method were applied to comparatively study the inorganic components in the sources and receptor samples.The results of factor analysis show that the major sources were road dust,waste incineration and mixed sources which contained automobile exhaust,soil dust/secondary dust and coal dust during the daytime in Longyan City,China.There are two major sources of pollution which are soil dust and mixture sources of automobile exhaust and secondary dust during the night in Longyan.The results of CMB show that the major sources are secondary dust,automobile exhaust and road dust during the daytime in Longyan.The major sources are secondary dust,soil dust and automobile exhaust during the night in Longyan.The results of the two methods are similar to each other and the results will guide us to plan to control the PM10 pollution sources in Longyan.展开更多
A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A ...A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.展开更多
The dispersed phase in multiphase flows can be modeled by the population balance model(PBM). A typical population balance equation(PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source...The dispersed phase in multiphase flows can be modeled by the population balance model(PBM). A typical population balance equation(PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source terms. The equation is therefore quite complex and difficult to solve analytically or numerically. The quadrature-based moment methods(QBMMs) are a class of methods that solve the PBE by converting the transport equation of the number density function(NDF) into moment transport equations. The unknown source terms are closed by numerical quadrature. Over the years, many QBMMs have been developed for different problems, such as the quadrature method of moments(QMOM), direct quadrature method of moments(DQMOM),extended quadrature method of moments(EQMOM), conditional quadrature method of moments(CQMOM),extended conditional quadrature method of moments(ECQMOM) and hyperbolic quadrature method of moments(Hy QMOM). In this paper, we present a comprehensive algorithm review of these QBMMs. The mathematical equations for spatially homogeneous systems with first-order point processes and second-order point processes are derived in detail. The algorithms are further extended to the inhomogeneous system for multiphase flows, in which the computational fluid dynamics(CFD) can be coupled with the PBE. The physical limitations and the challenging numerical problems of these QBMMs are discussed. Possible solutions are also summarized.展开更多
Due to global warming, glaciers on the Tibetan Plateau(TP) are experiencing widespread shrinkage; however, the mechanisms controlling glacier variations across the TP are still rather unclear, especially on the northe...Due to global warming, glaciers on the Tibetan Plateau(TP) are experiencing widespread shrinkage; however, the mechanisms controlling glacier variations across the TP are still rather unclear, especially on the northeastern TP. In this study, a physically based, distributed surface-energy and mass-balance model was used to simulate glacier mass balance forced by meteorological data. The model was applied to Laohugou No. 12 Glacier, western Qilian Mountains, China, during2010~2012. The simulated albedo and mass balance were validated and calibrated by in situ measurements. The simulated annual glacier-wide mass balances were-385 mm water equivalent(w.e.) in 2010/2011 and-232 mm w.e. in 2011/2012,respectively. The mean equilibrium-line altitude(ELA) was 5,015 m a.s.l., during 2010~2012, which ascended by 215 m compared to that in the 1970 s. The mean accumulation area ratio(AAR) was 39% during the two years. Climatic-sensitivity experiments indicated that the change of glacier mass balance resulting from a 1.5 °C increase in air temperature could be offset by a 30% increase in annual precipitation. The glacier mass balance varied linearly with precipitation, at a rate of130 mm w.e. per 10% change in total precipitation.展开更多
Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlight...Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.展开更多
An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primar...An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as "macro-joints",while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as "micro-defects".The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.展开更多
Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time(HB-AFT) domain technique has some advantages in dealing with nonlinear probl...Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time(HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.展开更多
Microseismic(MS)event locations are vital aspect of MS monitoring technology used to delineate the damage zone inside the surrounding rock mass.However,complex geological conditions can impose significantly adverse ef...Microseismic(MS)event locations are vital aspect of MS monitoring technology used to delineate the damage zone inside the surrounding rock mass.However,complex geological conditions can impose significantly adverse effects on the final location results.To achieve a high-accuracy location in a complex cavern-containing structure,this study develops an MS location method using the fast marching method(FMM)with a second-order difference approach(FMM2).Based on the established velocity model with three-dimensional(3D)discrete grids,the realization of the MS location can be achieved by searching the minimum residual between the theoretical and actual first arrival times.Moreover,based on the calculation results of FMM2,the propagation paths from the MS sources to MS sensors can be obtained using the linear interpolation approach and the Runge–Kutta method.These methods were validated through a series of numerical experiments.In addition,our proposed method was applied to locate the recorded blasting and MS events that occurred during the excavation period of the underground caverns at the Houziyan hydropower station.The location results of the blasting activities show that our method can effectively reduce the location error compared with the results based on the uniform velocity model.Furthermore,the obtained MS location was verified through the occurrence of shotcrete fractures and spalling,and the monitoring results of the in-situ multipoint extensometer.Our proposed method can offer a more accurate rock fracture location and facilitate the delineation of damage zones inside the surrounding rock mass.展开更多
Mass balance is a key indicator of the sensitivity of glaciers to climate change. Field measurement is one of the most important ways to study the mass balance of glaciers. Based on observations of mass balance in the...Mass balance is a key indicator of the sensitivity of glaciers to climate change. Field measurement is one of the most important ways to study the mass balance of glaciers. Based on observations of mass balance in the ablation zone of Shuiguan Glacier No.4, Qilian Mountains, China, combined with the balance ratio between accumulation and ablation, we established a linear relation between mass balance and altitude. The results show that the mean annual mass balance of this glacier was ~510 mm w.e. from 2010 to 2013. The uncertainty in the balance ratio value does not lead to a significant difference in the mass balance. The equilibrium-line altitude rose by 180 m from 1972 to 2013, while the accumulation–area ratio decreased from 0.68 to 0.25. These variations may be caused by changes in air temperature. Meanwhile, the glacier is at present not in a steady state, and it may continue to shrink by a further ~900 m, even without further climate warming. In the western Lenglongling Mountains, assuming that the glaciers are in a steady state and the Equilibrium-line altitudes(ELAs)remain similar, there will be only 46 glaciers left, covering a total area of 19.2 km^2, in other words, only 22.3% of the glaciers area in 1972.展开更多
A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearize...A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.展开更多
In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman pl...In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.展开更多
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
基金Project supported by the National Natural Science Foundation of China(Nos.11972129 and12372008)the National Major Science and Technology Projects of China(No.2017-IV-0008-0045)+3 种基金the Natural Science Foundation of Heilongjiang Province of China(No.YQ2022A008)the Fundamental Research Funds for the Central Universities of China(No.HIT.OCEF.2023006)the Polish National Science Centre of Poland under the OPUS 18 grant(No.2019/35/B/ST8/00980)the Tianjin University Independent Innovation Foundation of China(No.2023XJS-0038)。
文摘The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.
文摘A paired basin study in the upper Santa Fe River watershed following forest thinning and prescribed burns successfully measured water budget components in a treated and an untreated (control) basin. The paired basin study was established to investigate questions that have arisen regarding changes in water yield from forest treatments. Precipitation, stream flow, soil moisture, and chloride concentrations in precipitation and stream flow were measured to quantify the water budget components. The results from eleven years of data collection and analysis have a high degree of confidence with respect to measuring the water budget components based on the mass balance of water and chloride. The differences in the geologic structure and topography between the two paired basins appeared to impact the water budgets more than the forest treatments, except during periods when winter precipitation and snowmelt represented a significant component of inflow. Although this paired basin study was not able to portray a simple relationship between forest thinning and water yield, the chloride concentration methodology used to estimate evapotranspiration (ET) was successful. These detailed observations of chloride deposition and transport characteristics may be relevant for other researchers working in forested basins with substantial ET. ET rates were estimated by examining the cycle of chloride entering and exiting each basin over six integration periods. ET was estimated to be about 90% to 94% of precipitation in the treated basin and 77% to 86% in the control basin. The higher ET in the treated basin both before and after forest treatments may be due to the much greater area of west-facing hillslopes in the treated basin, which receive warm afternoon sun, and the greater area of rock cover in the control basin. Variation in the chloride concentration of collected precipitation samples from different sites indicates that horizontal precipitation of chloride in the tree canopy is an important consideration when using the chloride mass balance approach to calculate water budget components.
基金financial support by the National Natural Science Foundation of China(Grant Nos.52008152,U1965204,52061160367,U2067203 and 52008153)Natural Science Foundation of Hebei Province of China(Grant No.E2021202087)Hebei Department of Human Resource(Grant No.E2020050015)。
文摘Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the deformation properties of complex fractured rock mass.It comprehends both the advantages of the discrete fracture network model and the equivalent continuum model to capture the features of discontinuities explicitly while reducing computational intensity.The complex fracture network is stochastically split into a number of subfracture networks according to the domain,length or angle.An analytical solution is derived to infer theoretically the relationship between the elastic moduli of the original complex fractured rock mass and the split subfractured rock masses by introducing a correction term based on the deformation superposition principle.Numerical simulations are conducted to determine the elastic moduli of split subfractured rock masses using universal distinct element code(UDEC),while the elastic modulus of the original model is estimated based on the currently proposed analytical relationship.The results show that the estimation accuracy with the current domainbased splitting model is far superior compared to those with the other two splitting models.Thus,the estimation method of elastic modulus of complex fractured rock mass based on domain splitting mode of fracture network is identified as the multi-domain equivalent method proposed in this paper.The reliability of this method is evaluated,and its high computational efficiency is demonstrated through exemplification with regard to different geometric configurations for stochastically artificial discrete fracture network.The proposed multi-domain equivalent method constructs the theoretical framework except for the regression analysis hypothesis compared to the density-reduced model equivalent method.
文摘Glacier response patterns at the catchment scale are highly heterogeneous and defined by a complex interplay of various dynamics and surface factors.Previous studies have explained heterogeneous responses in qualitative ways but quantitative assessment is lacking yet where an intrazone homogeneous climate assumption can be valid.Hence,in the current study,the reason for heterogeneous mass balance has been explained in quantitative methods using a multiple linear regression model in the Sikkim Himalayan region.At first,the topographical parameters are selected from previously published studies,then the most significant topographical and geomorphological parameters are selected with backward stepwise subset selection methods.Finally,the contributions of selected parameters are calculated by least square methods.The results show that,the magnitude of mass balance lies between-0.003±0.24 to-1.029±0.24 m.w.e.a^(-1) between 2000 and 2020 in the Sikkim Himalaya region.Also,the study shows that,out of the terminus type of the glacier,glacier area,debris cover,ice-mixed debris,slope,aspect,mean elevation,and snout elevation of the glaciers,only the terminus type and mean elevation of the glacier are significantly altering the glacier mass balance in the Sikkim Himalayan region.Mathematically,the mass loss is approximately 0.40 m.w.e.a^(-1) higher in the lake-terminating glaciers compared to the land-terminating glaciers in the same elevation zone.On the other hand,a thousand meters mean elevation drop is associated with 0.179 m.w.e.a-1of mass loss despite the terminus type of the glaciers.In the current study,the model using the terminus type of the glaciers and the mean elevation of the glaciers explains 76% of fluctuation of mass balance in the Sikkim Himalayan region.
基金supported by National Key Research and Development Program of China(No.2021YFA0717100)NationalNatural Science Foundation of China(Nos.12072270,U2013206).
文摘The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.
基金supported by the National Natural Science Foundation of China(Grant No.52071200)the Science and Technology Commission of Shanghai Munici-pality.(Grant No.23010501900)。
文摘In order to develop a anchoring operation simulation system and improve safety during anchoring operations,a relatively accurate mathematical model of anchoring operations needs to be established.In this paper,the stress condition of anchor chain under environmental and subsea geological conditions is further studied and the stress condition of anchor chain is analyzed based on the previous research.In this paper,a quasi-static model based on catenary method is used as the basis of dynamic analysis,and the dynamic model of anchor chain is established based on the concentrated mass method,which fully considers the influence of anchor chain weight,hydrodynamic force,ocean current and interaction with the seabed.The fourth-order Runge Kutta method was used to solve the model numerically,and a calculation procedure was developed.The accuracy of the model was verified by comparing the calculated results with the experimental results,indicating that the constructed anchor chain dynamics model has a high accuracy.
基金Supported by the Natural Basic Research Program of China(No.2005CB422207)the Fund of Eco-enviromental Impacts and Protection in Devoloping and Utilizing of Oil-shale Resources(No.OSR-01-06)
文摘In order to identify the day and night pollution sources of PM10 in ambient air in Longyan City,the authors analyzed the elemental composition of respirable particulate matters in the day and night ambient air samples and various pollution sources which were collected in January 2010 in Longyan with inductivity coupled plasma-mass spectrometry(ICP-MS).Then chemical mass balance(CMB) model and factor analysis(FA) method were applied to comparatively study the inorganic components in the sources and receptor samples.The results of factor analysis show that the major sources were road dust,waste incineration and mixed sources which contained automobile exhaust,soil dust/secondary dust and coal dust during the daytime in Longyan City,China.There are two major sources of pollution which are soil dust and mixture sources of automobile exhaust and secondary dust during the night in Longyan.The results of CMB show that the major sources are secondary dust,automobile exhaust and road dust during the daytime in Longyan.The major sources are secondary dust,soil dust and automobile exhaust during the night in Longyan.The results of the two methods are similar to each other and the results will guide us to plan to control the PM10 pollution sources in Longyan.
基金support from the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No.2019319)support from the Start-up Foundation of Suzhou Institute of Nano-Tech and Nano-Bionics,CAS,Suzhou (Grant No.Y9AAD110)。
文摘A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.
文摘The dispersed phase in multiphase flows can be modeled by the population balance model(PBM). A typical population balance equation(PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source terms. The equation is therefore quite complex and difficult to solve analytically or numerically. The quadrature-based moment methods(QBMMs) are a class of methods that solve the PBE by converting the transport equation of the number density function(NDF) into moment transport equations. The unknown source terms are closed by numerical quadrature. Over the years, many QBMMs have been developed for different problems, such as the quadrature method of moments(QMOM), direct quadrature method of moments(DQMOM),extended quadrature method of moments(EQMOM), conditional quadrature method of moments(CQMOM),extended conditional quadrature method of moments(ECQMOM) and hyperbolic quadrature method of moments(Hy QMOM). In this paper, we present a comprehensive algorithm review of these QBMMs. The mathematical equations for spatially homogeneous systems with first-order point processes and second-order point processes are derived in detail. The algorithms are further extended to the inhomogeneous system for multiphase flows, in which the computational fluid dynamics(CFD) can be coupled with the PBE. The physical limitations and the challenging numerical problems of these QBMMs are discussed. Possible solutions are also summarized.
基金supported by the Chinese Academy of Sciences(KJZD-EW-G03-04)the National Natural Science Foundation of China(41721091,41671071)Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering(No.2017490711)
文摘Due to global warming, glaciers on the Tibetan Plateau(TP) are experiencing widespread shrinkage; however, the mechanisms controlling glacier variations across the TP are still rather unclear, especially on the northeastern TP. In this study, a physically based, distributed surface-energy and mass-balance model was used to simulate glacier mass balance forced by meteorological data. The model was applied to Laohugou No. 12 Glacier, western Qilian Mountains, China, during2010~2012. The simulated albedo and mass balance were validated and calibrated by in situ measurements. The simulated annual glacier-wide mass balances were-385 mm water equivalent(w.e.) in 2010/2011 and-232 mm w.e. in 2011/2012,respectively. The mean equilibrium-line altitude(ELA) was 5,015 m a.s.l., during 2010~2012, which ascended by 215 m compared to that in the 1970 s. The mean accumulation area ratio(AAR) was 39% during the two years. Climatic-sensitivity experiments indicated that the change of glacier mass balance resulting from a 1.5 °C increase in air temperature could be offset by a 30% increase in annual precipitation. The glacier mass balance varied linearly with precipitation, at a rate of130 mm w.e. per 10% change in total precipitation.
文摘Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.
文摘An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as "macro-joints",while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as "micro-defects".The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.
基金supported by the National Natural Science Foundation of China(No.10632040)
文摘Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time(HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.
基金the Key Program of National Natural Science Foundation of China(52039007)for providing financial support.
文摘Microseismic(MS)event locations are vital aspect of MS monitoring technology used to delineate the damage zone inside the surrounding rock mass.However,complex geological conditions can impose significantly adverse effects on the final location results.To achieve a high-accuracy location in a complex cavern-containing structure,this study develops an MS location method using the fast marching method(FMM)with a second-order difference approach(FMM2).Based on the established velocity model with three-dimensional(3D)discrete grids,the realization of the MS location can be achieved by searching the minimum residual between the theoretical and actual first arrival times.Moreover,based on the calculation results of FMM2,the propagation paths from the MS sources to MS sensors can be obtained using the linear interpolation approach and the Runge–Kutta method.These methods were validated through a series of numerical experiments.In addition,our proposed method was applied to locate the recorded blasting and MS events that occurred during the excavation period of the underground caverns at the Houziyan hydropower station.The location results of the blasting activities show that our method can effectively reduce the location error compared with the results based on the uniform velocity model.Furthermore,the obtained MS location was verified through the occurrence of shotcrete fractures and spalling,and the monitoring results of the in-situ multipoint extensometer.Our proposed method can offer a more accurate rock fracture location and facilitate the delineation of damage zones inside the surrounding rock mass.
基金financially supported by the Ministry of Science and Technology of the People’s Republic of China (No. 2013FY111400)National Natural Science Foundation of China (No.41471008+1 种基金 No. 41571003)Fundamental Research Funds for the Central Universities (lzujbky-2015-126)
文摘Mass balance is a key indicator of the sensitivity of glaciers to climate change. Field measurement is one of the most important ways to study the mass balance of glaciers. Based on observations of mass balance in the ablation zone of Shuiguan Glacier No.4, Qilian Mountains, China, combined with the balance ratio between accumulation and ablation, we established a linear relation between mass balance and altitude. The results show that the mean annual mass balance of this glacier was ~510 mm w.e. from 2010 to 2013. The uncertainty in the balance ratio value does not lead to a significant difference in the mass balance. The equilibrium-line altitude rose by 180 m from 1972 to 2013, while the accumulation–area ratio decreased from 0.68 to 0.25. These variations may be caused by changes in air temperature. Meanwhile, the glacier is at present not in a steady state, and it may continue to shrink by a further ~900 m, even without further climate warming. In the western Lenglongling Mountains, assuming that the glaciers are in a steady state and the Equilibrium-line altitudes(ELAs)remain similar, there will be only 46 glaciers left, covering a total area of 19.2 km^2, in other words, only 22.3% of the glaciers area in 1972.
文摘A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.
文摘In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.
