Many experiments have supported the contact models,such as the GW and MB models,but the majority of previous validations have been performed under light loads,resulting in a linear relationship between normal force an...Many experiments have supported the contact models,such as the GW and MB models,but the majority of previous validations have been performed under light loads,resulting in a linear relationship between normal force and contact area.However,the real contact area fraction should never equal one;there must be a limit smaller than the apparent area,implying that the real contact area cannot increase linearly indefinitely.In this paper,the real contact area between two polymethylmethacrylate(PMMA)blocks under heavy load is measured using the total reflection method,and the contact area is analyzed using the image processing method.The results show that the real contact area increases with normal load linearly in light loads but non-linearly in heavy loads;the number of contact spots increases with load linearly in light loads but also non-linearly in heavy loads,synchronous with the change in the real contact area.The GW,MB,and Zhao,Maietta,and Chang(ZMC)models were used to predict the experiment results,but none of them predicted the non-linear stage.A revised GW model based on the bulk deformation hypothesis performs better in predicting the non-linear stage.The study’s findings can be applied to PMMA or other similar materials,and they can serve as a useful reference for future research on the contact mechanisms of other materials.展开更多
Organisms have evolved a strain limiting mechanism,reflected as a non-linear elastic constitutive,to prevent large deformations from threatening soft tissue integrity.Compared with linear elastic substrates,the wrinkl...Organisms have evolved a strain limiting mechanism,reflected as a non-linear elastic constitutive,to prevent large deformations from threatening soft tissue integrity.Compared with linear elastic substrates,the wrinkle of films on non-linear elastic substrates has received less attention.In this article,a unique wrinkle evolution of the film-substrate system with a J-shaped non-linear stress-strain relation is reported.The result shows that a concave hexagonal array pattern is formed with the shrinkage strain of the film-substrate systems developing.As the interconnection of hexagonal arrays,a unit cell ridge network appears with properties such as chirality and helix.The subparagraph maze pattern formed with high compression is mainly composed of special single-cell ridge networks such as spiral single cores,chiral double cores,and combined multi-cores.This evolutionary model is highly consistent with the results of experiments,and it also predicts wrinkle morphology that has not yet been reported.These findings can serve as a novel explanation for the surface wrinkle of biological soft tissue,as well as provide references for the preparation of artificial biomaterials and programmable soft matter.展开更多
This opinion article discusses the original research work of Yünkül et al.(the Authors)published in the Journal of Mountain Science 21(9):3108–3122.Employing non-linear regression,fuzzy logic and artificial...This opinion article discusses the original research work of Yünkül et al.(the Authors)published in the Journal of Mountain Science 21(9):3108–3122.Employing non-linear regression,fuzzy logic and artificial neural network modeling techniques,the Authors interrogated a large database assembled from the existing research literature to assess the performance of twelve equation rules in predicting the undrained shear strength(s_(u))mobilized for remolded fine-grained soils at different values of liquidity index(I_(L))and water content ratio.Based on their analyses,the Authors proposed a simple and reportedly reliable correlation(i.e.,Eq.9 in their paper)for predicting s_(u) over the I_(L) range of 0.15 to 3.00.This article describes various shortcomings in the Authors’assembled database(including potentially anomalous data and covering an excessively wide I_(L) range in relation to routine geotechnical and transportation engineering applications)and their proposed s_(u)=f(I_(L))correlation.Contrary to the Authors’assertions,their proposed correlation is not reliable for fine-grained soils with consistencies in the general firm to stiff range(i.e.,for 0.15<I_(L)<0.40),increasingly overestimating s_(u) for reducing I_(L),and eventually predicting s_(u)→+∞for I_(L)→0.15+(while producing mathematically undefined s_(u) for I_(L)<0.15),thus rendering their correlation unconservative and potentially leading to unsafe geotechnical designs.Exponential or regular-power type s_(u)=f(I_(L))models are more s_(u)itable when developing correlations that are applicable over the full plastic range(of 0<I_(L)<1),thereby providing reasonably conservative s_(u) predictions for use in the preliminary design for routine geotechnical engineering applications.展开更多
Aimed at the doubly near-far problems in a large range suffered by the remote user group and in a small range existing in both nearby and remote user groups during energy harvesting and computation offloading,a resour...Aimed at the doubly near-far problems in a large range suffered by the remote user group and in a small range existing in both nearby and remote user groups during energy harvesting and computation offloading,a resource allocation method for unmanned aerial vehicle(UAV)-assisted and user cooperation non-linear energy harvesting mobile edge computing(MEC)system is proposed.The UAV equipped with an MEC server is introduced to provide energy and computing services for the remote user group to alleviate the doubly near-far problem in a large range suffered by the remote user group.The doubly near-far problem in a small range existing in both nearby and remote user groups is mitigated by user cooperation.The specific user cooperation strategy is that the user near the base station or the UAV is used as a relay to transfer the computing task of the user far from the base station or the UAV to the MEC server for computing.By jointly optimizing users’offloading time,users’transmitting power,and the hovering position of the UAV,the resource allocation problem is modeled as a nonlinear programming problem with the objective of maximizing computation efficiency.The suboptimal solution is obtained by adopting the differential evolution algorithm.Simulation results show that,compared with the resource allocation method based on genetic algorithm and the without user cooperation method,the proposed method has higher computation efficiency.展开更多
This study aims to predict the undrained shear strength of remolded soil samples using non-linear regression analyses,fuzzy logic,and artificial neural network modeling.A total of 1306 undrained shear strength results...This study aims to predict the undrained shear strength of remolded soil samples using non-linear regression analyses,fuzzy logic,and artificial neural network modeling.A total of 1306 undrained shear strength results from 230 different remolded soil test settings reported in 21 publications were collected,utilizing six different measurement devices.Although water content,plastic limit,and liquid limit were used as input parameters for fuzzy logic and artificial neural network modeling,liquidity index or water content ratio was considered as an input parameter for non-linear regression analyses.In non-linear regression analyses,12 different regression equations were derived for the prediction of undrained shear strength of remolded soil.Feed-Forward backpropagation and the TANSIG transfer function were used for artificial neural network modeling,while the Mamdani inference system was preferred with trapezoidal and triangular membership functions for fuzzy logic modeling.The experimental results of 914 tests were used for training of the artificial neural network models,196 for validation and 196 for testing.It was observed that the accuracy of the artificial neural network and fuzzy logic modeling was higher than that of the non-linear regression analyses.Furthermore,a simple and reliable regression equation was proposed for assessments of undrained shear strength values with higher coefficients of determination.展开更多
The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration(AA)algorithm t...The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration(AA)algorithm to fixed-point(FP) iteration method. It computes the approximation to the solutions at each iteration based on the history of vectors in extended space, which includes the vector of unknowns, the discrete form of the operator, and the equation's right-hand side. Several constraints are applied to AA algorithm, including a limitation of the time step variation during the iteration process, which allows switching to the base FP iterations to maintain convergence. Compared to the base FP algorithm, the improved version of the AA algorithm enables a reliable and rapid convergence of the iterative solution for the quasi-linear elliptic pressure equation describing the flow of particle-laden yield-stress fluids in a narrow channel during hydraulic fracturing, a key technology for stimulating hydrocarbon-bearing reservoirs. In particular, the proposed AA algorithm allows for faster computations and resolution of unyielding zones in hydraulic fractures that cannot be calculated using the FP algorithm. The quasi-linear elliptic pressure equation under consideration describes various physical processes, such as the displacement of fluids with viscoplastic rheology in a narrow cylindrical annulus during well cementing,the displacement of cross-linked gel in a proppant pack filling hydraulic fractures during the early stage of well production(fracture flowback), and multiphase filtration in a rock formation. We estimate computational complexity of the developed algorithm as compared to Jacobian-based algorithms and show that the performance of the former one is higher in modelling of flows of viscoplastic fluids. We believe that the developed algorithm is a useful numerical tool that can be implemented in commercial simulators to obtain fast and converged solutions to the non-linear problems described above.展开更多
Considering the adsorption loss of the hydraulic fracturing assisted oil displacement(HFAD)agent in the matrix,a method is proposed to characterize the dynamic saturation adsorption capacity of the HFAD agent with pre...Considering the adsorption loss of the hydraulic fracturing assisted oil displacement(HFAD)agent in the matrix,a method is proposed to characterize the dynamic saturation adsorption capacity of the HFAD agent with pressure differential and permeability.Coupled with the viscosity-concentration relationship of the HFAD agent,a non-linear seepage model of HFAD was established,taking into account the adsorption effect of high pressure drops,and the influencing factors were analyzed.The findings indicate that the replenishment of formation energy associated with HFAD technology is predominantly influenced by matrix permeability,fracture length and the initial concentration of the HFAD agent.The effect of replenishment of formation energy is positively correlated with matrix permeability and fracture length,and negatively correlated with the initial concentration of the HFAD agent.The initial concentration and injection amount of the high-pressure HFAD agent can enhance the concentration of the HFAD agent in the matrix and improve the efficiency of oil washing.However,a longer fracture is not conducive to maintaining the high concentration of the HFAD agent in the matrix.Furthermore,the fracture length and pump displacement are the direct factors affecting the fluid flow velocity in the matrix subsequent to HFAD.These factors can be utilized to control the location of the displacement phase front,and thus affect the swept area of HFAD.A reasonable selection of the aforementioned parameters can effectively supplement the formation energy,expand the swept volume of the HFAD agent,improve the recovery efficiency of HFAD,and reduce the development cost.展开更多
Wavelet transforms have been successfully used in seismic data processing with their ability for local time - frequency analysis. However, identification of directionality is limited because wavelet transform coeffici...Wavelet transforms have been successfully used in seismic data processing with their ability for local time - frequency analysis. However, identification of directionality is limited because wavelet transform coefficients reveal only three spatial orientations. Whereas the ridgelet transform has a superior capability for direction detection and the ability to process signals with linearly changing characteristics. In this paper, we present the issue of low signal-to-noise ratio （SNR） seismic data processing based on the ridgelet transform. Actual seismic data with low SNR from south China has been processed using ridgelet transforms to improve the SNR and the continuity of seismic events. The results show that the ridgelet transform is better than the wavelet transform for these tasks.展开更多
The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measuremen...The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measurements, selected area diffraction patterns （SADPs）, transmission electron microscopy （TEM）, and tensile tests. The relative resistivity was calculated to characterize the phase transformation of the experimental alloy during different cooling processes. The results show that at high temperatures, the microstructure evolutions change from the directional diffusion of Zn and Mg atoms to the precipitation of S phase, depending on the cooling rate. At medium temperatures, q phase nucleates on A13Zr dispersoids and grain boundaries under fast cooling conditions, while S phase precipitates under the slow cooling conditions. The strength and ductility of the aged alloy suffer a significant deterioration due to the heterogeneous precipitation in medium temperature range. At low temperatures, homogeneously nucleated GP zone, η′ and η phases precipitate.展开更多
Economic development,food security,and ecological preservation are important issues encountered by karst re-gions.Faced with complex natural and social dynamics,we attempted to explore how interdependence within socio...Economic development,food security,and ecological preservation are important issues encountered by karst re-gions.Faced with complex natural and social dynamics,we attempted to explore how interdependence within socio-ecological system(SES)shaped sustainability in this region.A SES framework was constructed and three scenarios were predesigned:economic priority scenario,food security scenario,and ecological protection sce-nario.The System Dynamics model was used to simulate and forecast the evolution across various scenarios within the SES from 2005 to 2035.Through the Production-Possibility Frontiers in combined scenarios,trade-offpotential was identified and quantified.The results showed that the decoupling between social and ecological subsystems can be weaken in economic priority scenario,while coupling between them can be strengthen in food security scenario and ecological protection scenario.Within the SES,combined scenario analyses further suggest that the rocky desertification rate and the urban-rural income ratio exhibit the least trade-offpotential and inten-sity in combined economic priority scenario and ecological protection scenario,and the Soil Conservation and Food Supply demonstrate the least trade-offpotential and intensity in combined economic priority scenario and food security scenario.We can conclude the ecological engineering plays a significant role in alleviating trade-offs within the SES,but the effectiveness is limited.In light of intertwined socio-ecological challenges,combining ecological engineering with adaptive adjustments is a crucial strategy to enhance SES resilience and promote sustainable development in the South China Karst.展开更多
In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′j...In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.展开更多
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa...In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.展开更多
Understanding the relationship between sediment and discharge is crucial for effective river management and water-sediment modeling,especially in the Brahmaputra River,one of the large transboundary rivers with high s...Understanding the relationship between sediment and discharge is crucial for effective river management and water-sediment modeling,especially in the Brahmaputra River,one of the large transboundary rivers with high sediment and discharge variability in South Asia.Current knowledge of sediment-water relations is constrained by limited data,hindering effective transboundary river management.Using multivariate linear regression,climate elasticity coefficient,and traditional sediment rating curve,this study is designed to compare the sediment-water relations of the upstream(Nuxia)and the downstream(Bahadurabad).The results reveal significant variability between the two stations.In the upstream Nuxia,the simulation strongly correlates with observed suspended sediment load(SSL)and discharge(Q)(Pearson's r of 0.62 and 0.68,respectively).Conversely,at downstream Bahadurabad,weaker correlations(r=0.31 for sediment and r=0.51 for discharge simulation)indicate a reduced relation.This contrast reflects the non-linear nature of sediment-discharge coupling along the river continuum,shaped by both climatic and anthropogenic influences.Elasticity(ε)analysis highlights the dominant role of precipitation in shaping sediment-water dynamics(εP-SSL=2.53,εP-Q=1.01)at Nuxia,while Bahadurabad(εP-SSL=0.41,εP-Q=0.82)reflects a reduced sensitivity,possibly due to sediment retention along the floodplain.Air temperature elasticity(εT-SSL,-0.15&-3.06 at Nuxia and Bahadurabad,respectively)reveals contrasting impacts,strongly negatively influencing sediment transport at Bahadurabad.These findings highlight the significance of spatial variability and climatic influences on sediment dynamics,underscoring the necessity for site-specific management strategies.The sediment rating curve(SRC)analysis reveals a strong relationship between sediment and discharge(R^(2)=0.88)at Nuxia and a relatively weaker relationship(R^(2)=0.14)at Bahadurabad,which demonstrates a lower sedimentdischarge coupling that could be affected by downstream factors such as sediment deposition,channel morphology,and anthropogenic activities.This study offers valuable insights into sediment-water dynamics,highlighting the importance of understanding nonlinear relationships in the Brahmaputra River.展开更多
In the context of climate change,countries in West Africa are faced with recurrent flooding with catastrophic consequences,that makes it imperative to have access to rainfall information on fine spatial and temporal s...In the context of climate change,countries in West Africa are faced with recurrent flooding with catastrophic consequences,that makes it imperative to have access to rainfall information on fine spatial and temporal scales for better monitoring and prediction of these phenomena,as could be provided by weather radars.Based on an extensive archive of data from the X-band polarimetric radar and rain gauges observations gathered during the intensive AMMA campaigns in 2006–2007 and the Megha-Tropiques satellite measurement validation programme in 2010 in West Africa,we(i)simulated jointly realistic data for polarimetric radar variables and rain intensity using copula,and(ii)assessed rain rate estimation methods based on neural network(NN)inversion techniques and non-linearly calibrated parametric algorithms.The assessment of rainfall rate retrieval by these estimators is carried out using the part of the observations database not employed for calibration steps.The multiparametric algorithms R(ZH,K_(DP))and R(Z_(DR),K_(DP))perform better than R(ZH,Z_(DR))and R(ZH,Z_(DR),K_(DP)),especially since they are calibrated using copulas with upper tail dependencies,with KGE ranging in 0.68–0.75 and 0.79–0.82,respectively versus ranges of 0.40–0.64 and 0.20–0.51,for the two latter estimators.The neural network-based estimators RNN(Z_(DR),K_(DP))and RNN(ZH,K_(DP)),show KGE score characteristics comparable to those obtained from the best parametric relations,specifically optimized for the synthetic copula-based dataset.However,the neural network-based estimators were shown to be more robust when applied to a specific rainfall event.More specifically,neural network-based estimators trained on synthetic data are sensitive to the copulas’ability to capture the dependence between the variables of interest over the entire distribution of joint values.This leads to a near-cancellation of sensitivity to variability in the raindrop size distribution,as shown the coefficients of correlation near 1,especially for RNN(Z_(DR),K_(DP)),and for less extent RNN(Z_(H),K_(DP)).展开更多
The relationship between the neighborhood environment and well-being is attracting increasingly attention from researchers and policymakers,as the goal of development has shift from economy to well-being.However,exist...The relationship between the neighborhood environment and well-being is attracting increasingly attention from researchers and policymakers,as the goal of development has shift from economy to well-being.However,existing literature predominantly adopts the utilitarian approach,understanding well-being as people’s feelings about their lives and viewing the neighborhood environment as resources that benefit well-being.The Capability Approach,a novel approach that conceptualize well-being as the freedoms to do or to be and regard environment as conversion factors that influence well-being,can offer new lens by incorporating human development in-to these topics.This paper proposes an alternative theoretical framework:well-being is conceptualized and measured by capability;neighborhood environment affects well-being by providing spatial services,functioning as environmental conversion factors,and serving as social conversion factors.We conducted a case study of Changshu City located in eastern China,utilizing multiple resource data,applying explainable artificial intelligence(XAI),namely eXtreme Gradient Boosting(XGBoost)and SHapley Additive exPlana-tions(SHAP).Our findings highlight the significance of viewing the neighborhood environment as a set of conversion factors,as it provides more explanatory power than providing spatial services.Compared to conventional research based on linear relationship as-sumption,our results demonstrate that the effects of neighborhood environment on well-being are non-linear,characterized by threshold effects and interaction effects.These insights are crucial for informing urban planning and public policy.This research enriches our un-derstanding of well-being,neighborhood environment,and their relationship as well as provides empirical evidence for the core concept of conversion factors in the capability approach.展开更多
Many policymakers have recognized rural digitalization as an emerging strategy to improve farmers’well-being.However,in the context of China,whether digital village construction is an effective and long-term way to a...Many policymakers have recognized rural digitalization as an emerging strategy to improve farmers’well-being.However,in the context of China,whether digital village construction is an effective and long-term way to achieve farmers’common prosperity has not been thoroughly explored.This study aims to construct a theoretical analysis framework for the impact of digital village construction on farmers’common prosperity and provide new empirical evidence from dynamic and spatial perspectives.The results indicated that China’s digital village construction effectively promoted the farmers’common prosperity,and agricultural productive service and agricultural science and technology innovation are significant mediating mechanisms.However,it is not yet long-term,as the marginal effect of digital village construction is diminishing.The spatial spillover effect of digital village construction is also more obvious than its direct effect.Digital village construction consistently plays a stronger enabling role in the western region and provinces with better conditions for agriculture.The results suggest that digital village construction in China can effectively reduce regional disparities.But establishing a long-term driving mechanism for digital village construction on farmers’common prosperity is another novel and pressing task that requires urgent attention.展开更多
Many countries throughout the world have experienced large earthquakes,which cause building damage or collapse.After such earthquakes,structures must be inspected rapidly to judge whether they are safe to reoccupy.To ...Many countries throughout the world have experienced large earthquakes,which cause building damage or collapse.After such earthquakes,structures must be inspected rapidly to judge whether they are safe to reoccupy.To facilitate the inspection process,the authors previously developed a rapid building safety assessment system using sparse acceleration measurements for steel framed buildings.The proposed system modeled nonlinearity in the measurement data using a calibrated simplified lumped-mass model and convolutional neural networks(CNNs),based on which the buildinglevel damage index was estimated rapidly after earthquakes.The proposed system was validated for a nonlinear 3D numerical model of a five-story steel building,and later for a large-scale specimen of an 18-story building in Japan tested on the E-Defense shaking table.However,the applicability of the safety assessment system for reinforced concrete(RC)structures with complex hysteretic material nonlinearity has yet to be explored;the previous approach based on a simplified lumpedmass model with a Bouc-Wen hysteretic model does not accurately represent the inherent nonlinear behavior and resulting damage states of RC structures.This study extends the rapid building safety assessment system to low-rise RC moment resisting frame structures representing typical residential apartments in Japan.First,a safety classification for RC structures based on a damage index consistent with the current state of practice is defined.Then,a 3D nonlinear numerical model of a two-story moment frame structure is created.A simplified lumped-mass nonlinear model is developed and calibrated using the 3D model,incorporating the Takeda degradation model for the RC material nonlinearity.This model is used to simulate the seismic response and associated damage sensitive features(DSF)for random ground motion.The resulting database of responses is used to train a convolutional neural network(CNN)that performs rapid safety assessment.The developed system is validated using the 3D nonlinear analysis model subjected to historical earthquakes.The results indicate the applicability of the proposed system for RC structures following seismic events.展开更多
Investors are always willing to receive more data.This has become especially true for the application of modern portfolio theory to the institutional asset allocation process,which requires quantitative estimates of r...Investors are always willing to receive more data.This has become especially true for the application of modern portfolio theory to the institutional asset allocation process,which requires quantitative estimates of risk and return.When long-term data series are unavailable for analysis,it has become common practice to use recent data only.The danger is that these data may not be representative of future performance.Although longer data series are of poorer quality,are difficult to obtain,and may reflect various political and economic regimes,they often paint a very different picture of emerging market performance.This paper presents an application of a stochastic non-linear optimization model of portfolios including transaction costs in the Brazilian financial market.In order to have that,portfolio theory and optimal control were used as theoretical basis.The first strategy tries to allocate the whole available wealth,not considering the risk associated to portfolio(deterministic result).In this case the investor obtained profits of 7.23%a month,taking into account the three risk aversion levels during the whole planning period.On the contrary,the results from the stochastic algorithm obtain profits of 1.34%a month and 18.06%a year,if the investor has low risk aversion.The profits would be 0.88%a month and 11.02%a year for a medium risk aversion investor.And with high risk aversion,the investor obtains 0.62%a month and 7.68%a year.展开更多
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is...The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.展开更多
A non-linear non-ideal model, taking into account non-linear competitive isotherms, axial dispersion, film mass transfer, intraparticle diffusion, and port periodic switching, was developed to simulate the dynamics of...A non-linear non-ideal model, taking into account non-linear competitive isotherms, axial dispersion, film mass transfer, intraparticle diffusion, and port periodic switching, was developed to simulate the dynamics of simulated moving bed chromatography (SMBC). The model equations were solved by a new efficient numerical technique of orthogonal collocation on finite elements with periodical movement of concentration vector. The simulated SMBC performance is in accordance with the experimental results reported in the literature for separation of l,1'-bi-2-naphthol enantiomers using SMBC. This model is useful for design, operation, optimization and scale-up of non-linear SMBC for chiral separations with significant non-ideal effects, especially for high solute concentration and small intraparticle diffusion coefficient or large chiral stationary phase particle.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11872033)Beijing Municipal Natural Science Foundation(Grant No.3172017)。
文摘Many experiments have supported the contact models,such as the GW and MB models,but the majority of previous validations have been performed under light loads,resulting in a linear relationship between normal force and contact area.However,the real contact area fraction should never equal one;there must be a limit smaller than the apparent area,implying that the real contact area cannot increase linearly indefinitely.In this paper,the real contact area between two polymethylmethacrylate(PMMA)blocks under heavy load is measured using the total reflection method,and the contact area is analyzed using the image processing method.The results show that the real contact area increases with normal load linearly in light loads but non-linearly in heavy loads;the number of contact spots increases with load linearly in light loads but also non-linearly in heavy loads,synchronous with the change in the real contact area.The GW,MB,and Zhao,Maietta,and Chang(ZMC)models were used to predict the experiment results,but none of them predicted the non-linear stage.A revised GW model based on the bulk deformation hypothesis performs better in predicting the non-linear stage.The study’s findings can be applied to PMMA or other similar materials,and they can serve as a useful reference for future research on the contact mechanisms of other materials.
基金This work was supported by the Youth Project of Hunan Provincial Department of Education(Grant No.22B0334)the Bridge and Tunnel Engineering Innovation Project of Changsha University of Science&Technology(Grant No.11ZDXK11)and the Practical Innovation and Entrepreneurship Capacity Improvement Plan of Changsha University of Science and Technology(Grant No.CLSJCX23029).
文摘Organisms have evolved a strain limiting mechanism,reflected as a non-linear elastic constitutive,to prevent large deformations from threatening soft tissue integrity.Compared with linear elastic substrates,the wrinkle of films on non-linear elastic substrates has received less attention.In this article,a unique wrinkle evolution of the film-substrate system with a J-shaped non-linear stress-strain relation is reported.The result shows that a concave hexagonal array pattern is formed with the shrinkage strain of the film-substrate systems developing.As the interconnection of hexagonal arrays,a unit cell ridge network appears with properties such as chirality and helix.The subparagraph maze pattern formed with high compression is mainly composed of special single-cell ridge networks such as spiral single cores,chiral double cores,and combined multi-cores.This evolutionary model is highly consistent with the results of experiments,and it also predicts wrinkle morphology that has not yet been reported.These findings can serve as a novel explanation for the surface wrinkle of biological soft tissue,as well as provide references for the preparation of artificial biomaterials and programmable soft matter.
文摘This opinion article discusses the original research work of Yünkül et al.(the Authors)published in the Journal of Mountain Science 21(9):3108–3122.Employing non-linear regression,fuzzy logic and artificial neural network modeling techniques,the Authors interrogated a large database assembled from the existing research literature to assess the performance of twelve equation rules in predicting the undrained shear strength(s_(u))mobilized for remolded fine-grained soils at different values of liquidity index(I_(L))and water content ratio.Based on their analyses,the Authors proposed a simple and reportedly reliable correlation(i.e.,Eq.9 in their paper)for predicting s_(u) over the I_(L) range of 0.15 to 3.00.This article describes various shortcomings in the Authors’assembled database(including potentially anomalous data and covering an excessively wide I_(L) range in relation to routine geotechnical and transportation engineering applications)and their proposed s_(u)=f(I_(L))correlation.Contrary to the Authors’assertions,their proposed correlation is not reliable for fine-grained soils with consistencies in the general firm to stiff range(i.e.,for 0.15<I_(L)<0.40),increasingly overestimating s_(u) for reducing I_(L),and eventually predicting s_(u)→+∞for I_(L)→0.15+(while producing mathematically undefined s_(u) for I_(L)<0.15),thus rendering their correlation unconservative and potentially leading to unsafe geotechnical designs.Exponential or regular-power type s_(u)=f(I_(L))models are more s_(u)itable when developing correlations that are applicable over the full plastic range(of 0<I_(L)<1),thereby providing reasonably conservative s_(u) predictions for use in the preliminary design for routine geotechnical engineering applications.
基金the National Natural Science Foundation of China(No.61871133)the Natural Science Foundation of Fujian Province(No.2021J01587)。
文摘Aimed at the doubly near-far problems in a large range suffered by the remote user group and in a small range existing in both nearby and remote user groups during energy harvesting and computation offloading,a resource allocation method for unmanned aerial vehicle(UAV)-assisted and user cooperation non-linear energy harvesting mobile edge computing(MEC)system is proposed.The UAV equipped with an MEC server is introduced to provide energy and computing services for the remote user group to alleviate the doubly near-far problem in a large range suffered by the remote user group.The doubly near-far problem in a small range existing in both nearby and remote user groups is mitigated by user cooperation.The specific user cooperation strategy is that the user near the base station or the UAV is used as a relay to transfer the computing task of the user far from the base station or the UAV to the MEC server for computing.By jointly optimizing users’offloading time,users’transmitting power,and the hovering position of the UAV,the resource allocation problem is modeled as a nonlinear programming problem with the objective of maximizing computation efficiency.The suboptimal solution is obtained by adopting the differential evolution algorithm.Simulation results show that,compared with the resource allocation method based on genetic algorithm and the without user cooperation method,the proposed method has higher computation efficiency.
文摘This study aims to predict the undrained shear strength of remolded soil samples using non-linear regression analyses,fuzzy logic,and artificial neural network modeling.A total of 1306 undrained shear strength results from 230 different remolded soil test settings reported in 21 publications were collected,utilizing six different measurement devices.Although water content,plastic limit,and liquid limit were used as input parameters for fuzzy logic and artificial neural network modeling,liquidity index or water content ratio was considered as an input parameter for non-linear regression analyses.In non-linear regression analyses,12 different regression equations were derived for the prediction of undrained shear strength of remolded soil.Feed-Forward backpropagation and the TANSIG transfer function were used for artificial neural network modeling,while the Mamdani inference system was preferred with trapezoidal and triangular membership functions for fuzzy logic modeling.The experimental results of 914 tests were used for training of the artificial neural network models,196 for validation and 196 for testing.It was observed that the accuracy of the artificial neural network and fuzzy logic modeling was higher than that of the non-linear regression analyses.Furthermore,a simple and reliable regression equation was proposed for assessments of undrained shear strength values with higher coefficients of determination.
基金partial financial support from Gazpromneft Science and Technology Center。
文摘The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration(AA)algorithm to fixed-point(FP) iteration method. It computes the approximation to the solutions at each iteration based on the history of vectors in extended space, which includes the vector of unknowns, the discrete form of the operator, and the equation's right-hand side. Several constraints are applied to AA algorithm, including a limitation of the time step variation during the iteration process, which allows switching to the base FP iterations to maintain convergence. Compared to the base FP algorithm, the improved version of the AA algorithm enables a reliable and rapid convergence of the iterative solution for the quasi-linear elliptic pressure equation describing the flow of particle-laden yield-stress fluids in a narrow channel during hydraulic fracturing, a key technology for stimulating hydrocarbon-bearing reservoirs. In particular, the proposed AA algorithm allows for faster computations and resolution of unyielding zones in hydraulic fractures that cannot be calculated using the FP algorithm. The quasi-linear elliptic pressure equation under consideration describes various physical processes, such as the displacement of fluids with viscoplastic rheology in a narrow cylindrical annulus during well cementing,the displacement of cross-linked gel in a proppant pack filling hydraulic fractures during the early stage of well production(fracture flowback), and multiphase filtration in a rock formation. We estimate computational complexity of the developed algorithm as compared to Jacobian-based algorithms and show that the performance of the former one is higher in modelling of flows of viscoplastic fluids. We believe that the developed algorithm is a useful numerical tool that can be implemented in commercial simulators to obtain fast and converged solutions to the non-linear problems described above.
基金Supported by the National Nature Science Foundation of China(52374035,52074087)Postdoctoral Natural Science Foundation of China(2021M690528)。
文摘Considering the adsorption loss of the hydraulic fracturing assisted oil displacement(HFAD)agent in the matrix,a method is proposed to characterize the dynamic saturation adsorption capacity of the HFAD agent with pressure differential and permeability.Coupled with the viscosity-concentration relationship of the HFAD agent,a non-linear seepage model of HFAD was established,taking into account the adsorption effect of high pressure drops,and the influencing factors were analyzed.The findings indicate that the replenishment of formation energy associated with HFAD technology is predominantly influenced by matrix permeability,fracture length and the initial concentration of the HFAD agent.The effect of replenishment of formation energy is positively correlated with matrix permeability and fracture length,and negatively correlated with the initial concentration of the HFAD agent.The initial concentration and injection amount of the high-pressure HFAD agent can enhance the concentration of the HFAD agent in the matrix and improve the efficiency of oil washing.However,a longer fracture is not conducive to maintaining the high concentration of the HFAD agent in the matrix.Furthermore,the fracture length and pump displacement are the direct factors affecting the fluid flow velocity in the matrix subsequent to HFAD.These factors can be utilized to control the location of the displacement phase front,and thus affect the swept area of HFAD.A reasonable selection of the aforementioned parameters can effectively supplement the formation energy,expand the swept volume of the HFAD agent,improve the recovery efficiency of HFAD,and reduce the development cost.
基金This paper is supported by China Petrochemical Key Project in the"11th Five-Year"Plan Technology and the Doctorate Fund of Ministry of Education of China (No.20050491504)
文摘Wavelet transforms have been successfully used in seismic data processing with their ability for local time - frequency analysis. However, identification of directionality is limited because wavelet transform coefficients reveal only three spatial orientations. Whereas the ridgelet transform has a superior capability for direction detection and the ability to process signals with linearly changing characteristics. In this paper, we present the issue of low signal-to-noise ratio （SNR） seismic data processing based on the ridgelet transform. Actual seismic data with low SNR from south China has been processed using ridgelet transforms to improve the SNR and the continuity of seismic events. The results show that the ridgelet transform is better than the wavelet transform for these tasks.
基金Project(2014GK2013)supported by the Science and Technology Program of Hunan Province,China
文摘The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measurements, selected area diffraction patterns （SADPs）, transmission electron microscopy （TEM）, and tensile tests. The relative resistivity was calculated to characterize the phase transformation of the experimental alloy during different cooling processes. The results show that at high temperatures, the microstructure evolutions change from the directional diffusion of Zn and Mg atoms to the precipitation of S phase, depending on the cooling rate. At medium temperatures, q phase nucleates on A13Zr dispersoids and grain boundaries under fast cooling conditions, while S phase precipitates under the slow cooling conditions. The strength and ductility of the aged alloy suffer a significant deterioration due to the heterogeneous precipitation in medium temperature range. At low temperatures, homogeneously nucleated GP zone, η′ and η phases precipitate.
基金supported by the National Key Research and Develop-ment Program of China(Grant No.2022YFF1300701)the Sichuan Science and Technology Program(Grant No.2022JDJQ0015).
文摘Economic development,food security,and ecological preservation are important issues encountered by karst re-gions.Faced with complex natural and social dynamics,we attempted to explore how interdependence within socio-ecological system(SES)shaped sustainability in this region.A SES framework was constructed and three scenarios were predesigned:economic priority scenario,food security scenario,and ecological protection sce-nario.The System Dynamics model was used to simulate and forecast the evolution across various scenarios within the SES from 2005 to 2035.Through the Production-Possibility Frontiers in combined scenarios,trade-offpotential was identified and quantified.The results showed that the decoupling between social and ecological subsystems can be weaken in economic priority scenario,while coupling between them can be strengthen in food security scenario and ecological protection scenario.Within the SES,combined scenario analyses further suggest that the rocky desertification rate and the urban-rural income ratio exhibit the least trade-offpotential and inten-sity in combined economic priority scenario and ecological protection scenario,and the Soil Conservation and Food Supply demonstrate the least trade-offpotential and intensity in combined economic priority scenario and food security scenario.We can conclude the ecological engineering plays a significant role in alleviating trade-offs within the SES,but the effectiveness is limited.In light of intertwined socio-ecological challenges,combining ecological engineering with adaptive adjustments is a crucial strategy to enhance SES resilience and promote sustainable development in the South China Karst.
基金supported by the National Natural Science Foundation of China(No.12001117)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515110654).
文摘In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.
文摘In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
基金jointly supported by the Second Tibetan Plateau Scientific Expedition and Research Program(Grant No.2019QZKK0902)National Natural Science Foundation of China(NSFC)project(Grant No.42305178)+1 种基金the Key R&D Program of Tibet Autonomous Region(Grant No.XZ202301ZY0039G)the Science and Technology Research Program of Institute of Mountain Hazards and Environment,Chinese Academy of Sciences(Grant No.IMHEZDRW-01)。
文摘Understanding the relationship between sediment and discharge is crucial for effective river management and water-sediment modeling,especially in the Brahmaputra River,one of the large transboundary rivers with high sediment and discharge variability in South Asia.Current knowledge of sediment-water relations is constrained by limited data,hindering effective transboundary river management.Using multivariate linear regression,climate elasticity coefficient,and traditional sediment rating curve,this study is designed to compare the sediment-water relations of the upstream(Nuxia)and the downstream(Bahadurabad).The results reveal significant variability between the two stations.In the upstream Nuxia,the simulation strongly correlates with observed suspended sediment load(SSL)and discharge(Q)(Pearson's r of 0.62 and 0.68,respectively).Conversely,at downstream Bahadurabad,weaker correlations(r=0.31 for sediment and r=0.51 for discharge simulation)indicate a reduced relation.This contrast reflects the non-linear nature of sediment-discharge coupling along the river continuum,shaped by both climatic and anthropogenic influences.Elasticity(ε)analysis highlights the dominant role of precipitation in shaping sediment-water dynamics(εP-SSL=2.53,εP-Q=1.01)at Nuxia,while Bahadurabad(εP-SSL=0.41,εP-Q=0.82)reflects a reduced sensitivity,possibly due to sediment retention along the floodplain.Air temperature elasticity(εT-SSL,-0.15&-3.06 at Nuxia and Bahadurabad,respectively)reveals contrasting impacts,strongly negatively influencing sediment transport at Bahadurabad.These findings highlight the significance of spatial variability and climatic influences on sediment dynamics,underscoring the necessity for site-specific management strategies.The sediment rating curve(SRC)analysis reveals a strong relationship between sediment and discharge(R^(2)=0.88)at Nuxia and a relatively weaker relationship(R^(2)=0.14)at Bahadurabad,which demonstrates a lower sedimentdischarge coupling that could be affected by downstream factors such as sediment deposition,channel morphology,and anthropogenic activities.This study offers valuable insights into sediment-water dynamics,highlighting the importance of understanding nonlinear relationships in the Brahmaputra River.
文摘In the context of climate change,countries in West Africa are faced with recurrent flooding with catastrophic consequences,that makes it imperative to have access to rainfall information on fine spatial and temporal scales for better monitoring and prediction of these phenomena,as could be provided by weather radars.Based on an extensive archive of data from the X-band polarimetric radar and rain gauges observations gathered during the intensive AMMA campaigns in 2006–2007 and the Megha-Tropiques satellite measurement validation programme in 2010 in West Africa,we(i)simulated jointly realistic data for polarimetric radar variables and rain intensity using copula,and(ii)assessed rain rate estimation methods based on neural network(NN)inversion techniques and non-linearly calibrated parametric algorithms.The assessment of rainfall rate retrieval by these estimators is carried out using the part of the observations database not employed for calibration steps.The multiparametric algorithms R(ZH,K_(DP))and R(Z_(DR),K_(DP))perform better than R(ZH,Z_(DR))and R(ZH,Z_(DR),K_(DP)),especially since they are calibrated using copulas with upper tail dependencies,with KGE ranging in 0.68–0.75 and 0.79–0.82,respectively versus ranges of 0.40–0.64 and 0.20–0.51,for the two latter estimators.The neural network-based estimators RNN(Z_(DR),K_(DP))and RNN(ZH,K_(DP)),show KGE score characteristics comparable to those obtained from the best parametric relations,specifically optimized for the synthetic copula-based dataset.However,the neural network-based estimators were shown to be more robust when applied to a specific rainfall event.More specifically,neural network-based estimators trained on synthetic data are sensitive to the copulas’ability to capture the dependence between the variables of interest over the entire distribution of joint values.This leads to a near-cancellation of sensitivity to variability in the raindrop size distribution,as shown the coefficients of correlation near 1,especially for RNN(Z_(DR),K_(DP)),and for less extent RNN(Z_(H),K_(DP)).
基金Under the auspices of National Natural Science Foundation of China(No.42271230,42330510)。
文摘The relationship between the neighborhood environment and well-being is attracting increasingly attention from researchers and policymakers,as the goal of development has shift from economy to well-being.However,existing literature predominantly adopts the utilitarian approach,understanding well-being as people’s feelings about their lives and viewing the neighborhood environment as resources that benefit well-being.The Capability Approach,a novel approach that conceptualize well-being as the freedoms to do or to be and regard environment as conversion factors that influence well-being,can offer new lens by incorporating human development in-to these topics.This paper proposes an alternative theoretical framework:well-being is conceptualized and measured by capability;neighborhood environment affects well-being by providing spatial services,functioning as environmental conversion factors,and serving as social conversion factors.We conducted a case study of Changshu City located in eastern China,utilizing multiple resource data,applying explainable artificial intelligence(XAI),namely eXtreme Gradient Boosting(XGBoost)and SHapley Additive exPlana-tions(SHAP).Our findings highlight the significance of viewing the neighborhood environment as a set of conversion factors,as it provides more explanatory power than providing spatial services.Compared to conventional research based on linear relationship as-sumption,our results demonstrate that the effects of neighborhood environment on well-being are non-linear,characterized by threshold effects and interaction effects.These insights are crucial for informing urban planning and public policy.This research enriches our un-derstanding of well-being,neighborhood environment,and their relationship as well as provides empirical evidence for the core concept of conversion factors in the capability approach.
基金Under the auspices of National Natural Science Foundation of China(No.42171206,42071159),Regular Research Projects of Xi Jinping Thought on Socialism with Chinese Characteristics for a New Era Research Center of Zhejiang Province in 2025(No.25CCG32),Regularly Project of Social Science Research in Linping District,Hangzhou(No.Lpsk25C05),Xuezhi Professor Team at the College of Applied Arts and Science of Beijing Union University(No.BUUCAS-XZJSTD-2024004),Zhejiang Provincial Science and Technology Innovation Program for College Students(No.2024R408B065,2024R408A072)。
文摘Many policymakers have recognized rural digitalization as an emerging strategy to improve farmers’well-being.However,in the context of China,whether digital village construction is an effective and long-term way to achieve farmers’common prosperity has not been thoroughly explored.This study aims to construct a theoretical analysis framework for the impact of digital village construction on farmers’common prosperity and provide new empirical evidence from dynamic and spatial perspectives.The results indicated that China’s digital village construction effectively promoted the farmers’common prosperity,and agricultural productive service and agricultural science and technology innovation are significant mediating mechanisms.However,it is not yet long-term,as the marginal effect of digital village construction is diminishing.The spatial spillover effect of digital village construction is also more obvious than its direct effect.Digital village construction consistently plays a stronger enabling role in the western region and provinces with better conditions for agriculture.The results suggest that digital village construction in China can effectively reduce regional disparities.But establishing a long-term driving mechanism for digital village construction on farmers’common prosperity is another novel and pressing task that requires urgent attention.
基金supported by a fellowship from Design Department of Taisei Corporation。
文摘Many countries throughout the world have experienced large earthquakes,which cause building damage or collapse.After such earthquakes,structures must be inspected rapidly to judge whether they are safe to reoccupy.To facilitate the inspection process,the authors previously developed a rapid building safety assessment system using sparse acceleration measurements for steel framed buildings.The proposed system modeled nonlinearity in the measurement data using a calibrated simplified lumped-mass model and convolutional neural networks(CNNs),based on which the buildinglevel damage index was estimated rapidly after earthquakes.The proposed system was validated for a nonlinear 3D numerical model of a five-story steel building,and later for a large-scale specimen of an 18-story building in Japan tested on the E-Defense shaking table.However,the applicability of the safety assessment system for reinforced concrete(RC)structures with complex hysteretic material nonlinearity has yet to be explored;the previous approach based on a simplified lumpedmass model with a Bouc-Wen hysteretic model does not accurately represent the inherent nonlinear behavior and resulting damage states of RC structures.This study extends the rapid building safety assessment system to low-rise RC moment resisting frame structures representing typical residential apartments in Japan.First,a safety classification for RC structures based on a damage index consistent with the current state of practice is defined.Then,a 3D nonlinear numerical model of a two-story moment frame structure is created.A simplified lumped-mass nonlinear model is developed and calibrated using the 3D model,incorporating the Takeda degradation model for the RC material nonlinearity.This model is used to simulate the seismic response and associated damage sensitive features(DSF)for random ground motion.The resulting database of responses is used to train a convolutional neural network(CNN)that performs rapid safety assessment.The developed system is validated using the 3D nonlinear analysis model subjected to historical earthquakes.The results indicate the applicability of the proposed system for RC structures following seismic events.
文摘Investors are always willing to receive more data.This has become especially true for the application of modern portfolio theory to the institutional asset allocation process,which requires quantitative estimates of risk and return.When long-term data series are unavailable for analysis,it has become common practice to use recent data only.The danger is that these data may not be representative of future performance.Although longer data series are of poorer quality,are difficult to obtain,and may reflect various political and economic regimes,they often paint a very different picture of emerging market performance.This paper presents an application of a stochastic non-linear optimization model of portfolios including transaction costs in the Brazilian financial market.In order to have that,portfolio theory and optimal control were used as theoretical basis.The first strategy tries to allocate the whole available wealth,not considering the risk associated to portfolio(deterministic result).In this case the investor obtained profits of 7.23%a month,taking into account the three risk aversion levels during the whole planning period.On the contrary,the results from the stochastic algorithm obtain profits of 1.34%a month and 18.06%a year,if the investor has low risk aversion.The profits would be 0.88%a month and 11.02%a year for a medium risk aversion investor.And with high risk aversion,the investor obtains 0.62%a month and 7.68%a year.
基金Project supported by the National Natural Science Foundation of China (No. 10472060)Natural Science Founda-tion of Shanghai Municipality (No. 04ZR14058)Doctor Start-up Foundation of Shenyang Institute of Aeronautical Engineering (No. 05YB04).
文摘The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
基金Supported by the National Natural Science Foundation of China(No.20206027)and the Natural Science Foundation of Zhejiang Province(No.202046).
文摘A non-linear non-ideal model, taking into account non-linear competitive isotherms, axial dispersion, film mass transfer, intraparticle diffusion, and port periodic switching, was developed to simulate the dynamics of simulated moving bed chromatography (SMBC). The model equations were solved by a new efficient numerical technique of orthogonal collocation on finite elements with periodical movement of concentration vector. The simulated SMBC performance is in accordance with the experimental results reported in the literature for separation of l,1'-bi-2-naphthol enantiomers using SMBC. This model is useful for design, operation, optimization and scale-up of non-linear SMBC for chiral separations with significant non-ideal effects, especially for high solute concentration and small intraparticle diffusion coefficient or large chiral stationary phase particle.
