This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depen...This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.展开更多
Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but t...Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.展开更多
The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(...The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(GEP).Based on statistical reasoning,individual models were developed for two topographies:free-face and gently sloping ground.Along with a comparison with conventional approaches for predicting the Dh,four additional regression-based soft computing models,i.e.Gaussian process regression(GPR),relevance vector machine(RVM),sequential minimal optimization regression(SMOR),and M5-tree,were developed and compared with the GEP model.The results indicate that the GEP models predict Dh with less bias,as evidenced by the root mean square error(RMSE)and mean absolute error(MAE)for training(i.e.1.092 and 0.815;and 0.643 and 0.526)and for testing(i.e.0.89 and 0.705;and 0.773 and 0.573)in free-face and gently sloping ground topographies,respectively.The overall performance for the free-face topology was ranked as follows:GEP>RVM>M5-tree>GPR>SMOR,with a total score of 40,32,24,15,and 10,respectively.For the gently sloping condition,the performance was ranked as follows:GEP>RVM>GPR>M5-tree>SMOR with a total score of 40,32,21,19,and 8,respectively.Finally,the results of the sensitivity analysis showed that for both free-face and gently sloping ground,the liquefiable layer thickness(T_(15))was the major parameter with percentage deterioration(%D)value of 99.15 and 90.72,respectively.展开更多
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o...A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.展开更多
In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are...In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.展开更多
In groundwater hydrology,aquitard heterogeneity is often less considered compared to aquifers,despite its significant impact on groundwater hydraulics and groundwater resources evaluation.A semi-analytical solution is...In groundwater hydrology,aquitard heterogeneity is often less considered compared to aquifers,despite its significant impact on groundwater hydraulics and groundwater resources evaluation.A semi-analytical solution is derived for pumping-induced well hydraulics and groundwater budget with consideration of vertical heterogeneity in aquitard hydraulic conductivity(K)and specific storage(S_(s)).The proposed new solution is innovative in its partitioning of the aquitard into multiple homogeneous sub-layers to enable consideration of various forms of vertically heterogeneous K or S_(s).Two scenarios of analytical investigations are explored:one is the presence of aquitard interlayers with distinct K or S_(s) values,a common field-scale occurrence;another is an exponentially depth-decaying aquitard S_(s),a regional-scale phenomenon supported by statistical analysis.Analytical investigations reveal that a low-K interlayer can significantly increase aquifer drawdown and enhance aquifer/aquitard depletion;a high-S_(s) interlayer can noticeably reduce aquifer drawdown and increase aquitard depletion.Locations of low-K or high-S_(s) interlayers also significantly impact well hydraulics and groundwater budget.In the context of an exponentially depth-decaying aquitard S_(s),a larger decay exponent can enhance aquifer drawdown.When using current models with a vertically homogeneous aquitard,half the sum of the geometric and harmonic means of exponentially depth-decaying aquitard S_(s) should be used to calculate aquitard depletion and unconfined aquifer leakage.展开更多
This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ...This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.展开更多
The wadi dahab delta is in a dry, arid coastal zone within Egypt’s south Sinai Peninsula’s eastern portion. The primary water source is the Quaternary coastal alluvial aquifer. The groundwater salinity varies from 8...The wadi dahab delta is in a dry, arid coastal zone within Egypt’s south Sinai Peninsula’s eastern portion. The primary water source is the Quaternary coastal alluvial aquifer. The groundwater salinity varies from 890to 8213 mg/L, with a mean value of 3417 mg/L. The dissolved major ions have been used to calculate the seawater mixing index(SWMI) using a linear equation that discriminates the groundwater mostly affected by water–rock interaction(SWMI 1>) and other samples mixed with Seawater(SWMI < 1). The isotopic composition of groundwater for specifically chosen groundwater samples ranges from-0.645‰ to +5.212‰ for δ^(18)O and from-9.582‰ to + 22.778‰ for δ^(2)H, where the seawater represented by a Red Sea water sample(δ^(18)O + 1.64‰-δ^(2)H + 9.80‰) and reject brine water are considerably enriched the isotopic groundwater values. The geochemical NETPATH model constrained by the dissolved significant ions, isotopes, and the rock aquifer forming minerals as phases indicate the mixing percent with the seawater ranges from 9% to 97% of seawater from 91% to 3% of original recharge water. According to the SEAWAT 3-D flow models, seawater has penetrated the Northeastern Dahab delta aquifer, with the intrusion zone extending1500 m inland. The salt dissolution, upwelling of saline water, recharge from the upstream mountain block, and seawater encroachment are the primary aspects contributing to the deterioration of groundwater quality. These findings may have significance for effective groundwater withdrawal management in arid locations worldwide with similar hydrogeological systems.展开更多
In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized pr...In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.展开更多
In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate pro...In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.展开更多
On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear ...On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].展开更多
Background:Cancer-related fatigue(CRF)is a common and debilitating symptom experienced by patients with advanced-stage cancer,especially those undergoing antitumor therapy.This study aimed to evaluate the efficacy and...Background:Cancer-related fatigue(CRF)is a common and debilitating symptom experienced by patients with advanced-stage cancer,especially those undergoing antitumor therapy.This study aimed to evaluate the efficacy and safety of Renshenguben(RSGB)oral solution,a ginseng-based traditional Chinese medicine,in alleviating CRF in patients with advanced hepatocellular carcinoma(HCC)receiving antitumor treatment.Methods:In this prospective,open-label,controlled,multicenter study,patients with advanced HCC at BCLC stage C and a brief fatigue inventory(BFI)score of≥4 were enrolled.Participants were assigned to the RSGB group(RSGB,10 mL twice daily)or the control group(with supportive care).Primary and secondary endpoints were the change in multidimensional fatigue inventory(MFI)score,and BFI and functional assessment of cancer therapy-hepatobiliary(FACT-Hep)scores at weeks 4 and 8 after enrollment.Adverse events(AEs)and toxicities were assessed.Results:A total of 409 participants were enrolled,with 206 assigned to the RSGB group.At week 4,there was a trend towards improvement,but the differences were not statistically significant.At week 8,the RSGB group exhibited a significantly lower MFI score(P<0.05)compared to the control group,indicating improved fatigue levels.Additionally,the RSGB group showed significantly greater decrease in BFI and FACT-Hep scores at week 8(P<0.05).Subgroup analyses among patients receiving various antitumor treatments showed similar results.Multivariate linear regression analyses revealed that the RSGB group experienced a significantly substantial decrease in MFI,BFI,and FACT-Hep scores at week 8.No serious drug-related AEs or toxicities were observed.Conclusions:RSGB oral solution effectively reduced CRF in patients with advanced HCC undergoing antitumor therapy over an eight-week period,with no discernible toxicities.These findings support the potential of RSGB oral solution as an adjunctive treatment for managing CRF in this patient population.展开更多
Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained thro...Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.展开更多
Cyclic loads generated by environmental factors,such as winds,waves,and trains,will likely lead to performance degradation in pile foundations,resulting in issues like permanent displacement accumulation and bearing c...Cyclic loads generated by environmental factors,such as winds,waves,and trains,will likely lead to performance degradation in pile foundations,resulting in issues like permanent displacement accumulation and bearing capacity attenuation.This paper presents a semi-analytical solution for predicting the axial cyclic behavior of piles in sands.The solution relies on two enhanced nonlinear load-transfer models considering stress-strain hysteresis and cyclic degradation in the pile-soil interaction.Model parameters are calibrated through cyclic shear tests of the sand-steel interface and laboratory geotechnical testing of sands.A novel aspect involves the meticulous formulation of the shaft loadtransfer function using an interface constitutive model,which inherently inherits the interface model’s advantages,such as capturing hysteresis,hardening,degradation,and particle breakage.The semi-analytical solution is computed numerically using the matrix displacement method,and the calculated values are validated through model tests performed on non-displacement and displacement piles in sands.The results demonstrate that the predicted values show excellent agreement with the measured values for both the static and cyclic responses of piles in sands.The displacement pile response,including factors such as bearing capacity,mobilized shaft resistance,and convergence rate of permanent settlement,exhibit improvements compared to non-displacement piles attributed to the soil squeezing effect.This methodology presents an innovative analytical framework,allowing for integrating cyclic interface models into the theoretical investigation of pile responses.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
The performance and reliability of ferroelectric thin films at temperatures around a few Kelvin are critical for their application in cryo-electronics.In this work,TiN/Hf_(0.5)Zr_(0.5)O_(2)/TiN capacitors that are fre...The performance and reliability of ferroelectric thin films at temperatures around a few Kelvin are critical for their application in cryo-electronics.In this work,TiN/Hf_(0.5)Zr_(0.5)O_(2)/TiN capacitors that are free from the wake-up effect are investigated systematically from room temperature(300 K)to cryogenic temperature(30 K).We observe a consistent decrease in permittivity(εr)and a progressive increase in coercive electric field(Ec)as temperatures decrease.Our investigation reveals exceptional stability in the double remnant polarization(2P_(r))of our ferroelectric thin films across a wide temperature range.Specifically,at 30 K,a 2P_(r)of 36μC/cm^(2)under an applied electric field of 3.0 MV/cm is achieved.Moreover,we observed a reduced fatigue effect at 30 K in comparison to 300 K.The stable ferroelectric properties and endurance characteristics demonstrate the feasibility of utilizing HfO_(2)based ferroelectric thin films for cryo-electronics applications.展开更多
In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the ...In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.展开更多
We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the correspon...We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.展开更多
Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with th...Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.展开更多
基金supported by the Key Project of the NSFC(12131010)the NSFC(11771155,12271032)+1 种基金the NSF of Guangdong Province(2021A1515010249,2021A1515010303)supported by the NSFC(11971179,12371205)。
文摘This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.
基金funding support from the science and technology innovation Program of Hunan Province(Grant No.2023RC1017)Hunan Provincial Postgraduate Research and Innovation Project(Grant No.CX20220109)National Natural Science Foundation of China Youth Fund(Grant No.52208378).
文摘Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.
文摘The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(GEP).Based on statistical reasoning,individual models were developed for two topographies:free-face and gently sloping ground.Along with a comparison with conventional approaches for predicting the Dh,four additional regression-based soft computing models,i.e.Gaussian process regression(GPR),relevance vector machine(RVM),sequential minimal optimization regression(SMOR),and M5-tree,were developed and compared with the GEP model.The results indicate that the GEP models predict Dh with less bias,as evidenced by the root mean square error(RMSE)and mean absolute error(MAE)for training(i.e.1.092 and 0.815;and 0.643 and 0.526)and for testing(i.e.0.89 and 0.705;and 0.773 and 0.573)in free-face and gently sloping ground topographies,respectively.The overall performance for the free-face topology was ranked as follows:GEP>RVM>M5-tree>GPR>SMOR,with a total score of 40,32,24,15,and 10,respectively.For the gently sloping condition,the performance was ranked as follows:GEP>RVM>GPR>M5-tree>SMOR with a total score of 40,32,21,19,and 8,respectively.Finally,the results of the sensitivity analysis showed that for both free-face and gently sloping ground,the liquefiable layer thickness(T_(15))was the major parameter with percentage deterioration(%D)value of 99.15 and 90.72,respectively.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.
基金supported by the NSFC (12071438)supported by the NSFC (12201232)
文摘In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.
基金financially supported by the National Key Research and Development Program of China(Grant No.2019YFC1804301)the National Science Fourdation of China(Grant No.42272279,41902244)partial support from a Discovery Grant awarded by the Natural Sciences and Engineering Research Council of Canada(NSERC)。
文摘In groundwater hydrology,aquitard heterogeneity is often less considered compared to aquifers,despite its significant impact on groundwater hydraulics and groundwater resources evaluation.A semi-analytical solution is derived for pumping-induced well hydraulics and groundwater budget with consideration of vertical heterogeneity in aquitard hydraulic conductivity(K)and specific storage(S_(s)).The proposed new solution is innovative in its partitioning of the aquitard into multiple homogeneous sub-layers to enable consideration of various forms of vertically heterogeneous K or S_(s).Two scenarios of analytical investigations are explored:one is the presence of aquitard interlayers with distinct K or S_(s) values,a common field-scale occurrence;another is an exponentially depth-decaying aquitard S_(s),a regional-scale phenomenon supported by statistical analysis.Analytical investigations reveal that a low-K interlayer can significantly increase aquifer drawdown and enhance aquifer/aquitard depletion;a high-S_(s) interlayer can noticeably reduce aquifer drawdown and increase aquitard depletion.Locations of low-K or high-S_(s) interlayers also significantly impact well hydraulics and groundwater budget.In the context of an exponentially depth-decaying aquitard S_(s),a larger decay exponent can enhance aquifer drawdown.When using current models with a vertically homogeneous aquitard,half the sum of the geometric and harmonic means of exponentially depth-decaying aquitard S_(s) should be used to calculate aquitard depletion and unconfined aquifer leakage.
基金supported by the National Natural Science Foundation of China(12301251,12271232)the Natural Science Foundation of Shandong Province,China(ZR2021QA038)the Scientific Research Foundation of Linyi University,China(LYDX2020BS014)。
文摘This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.
文摘The wadi dahab delta is in a dry, arid coastal zone within Egypt’s south Sinai Peninsula’s eastern portion. The primary water source is the Quaternary coastal alluvial aquifer. The groundwater salinity varies from 890to 8213 mg/L, with a mean value of 3417 mg/L. The dissolved major ions have been used to calculate the seawater mixing index(SWMI) using a linear equation that discriminates the groundwater mostly affected by water–rock interaction(SWMI 1>) and other samples mixed with Seawater(SWMI < 1). The isotopic composition of groundwater for specifically chosen groundwater samples ranges from-0.645‰ to +5.212‰ for δ^(18)O and from-9.582‰ to + 22.778‰ for δ^(2)H, where the seawater represented by a Red Sea water sample(δ^(18)O + 1.64‰-δ^(2)H + 9.80‰) and reject brine water are considerably enriched the isotopic groundwater values. The geochemical NETPATH model constrained by the dissolved significant ions, isotopes, and the rock aquifer forming minerals as phases indicate the mixing percent with the seawater ranges from 9% to 97% of seawater from 91% to 3% of original recharge water. According to the SEAWAT 3-D flow models, seawater has penetrated the Northeastern Dahab delta aquifer, with the intrusion zone extending1500 m inland. The salt dissolution, upwelling of saline water, recharge from the upstream mountain block, and seawater encroachment are the primary aspects contributing to the deterioration of groundwater quality. These findings may have significance for effective groundwater withdrawal management in arid locations worldwide with similar hydrogeological systems.
文摘In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.
基金This study was supported by Basic Research Project from Jiangmen Science and Technology Bureau(Grant No.2220002000356)China University of Petroleum(Beijing)(Grand No.2462023BJRC007)The Guangdong Basic and Applied Basic Research Foundation(No.2022A1515110376).
文摘In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.
基金Supported by the National Natural Science Foundation of China(12261023,11861023)the Foundation of Science and Technology project of Guizhou Province of China([2018]5769-05)。
文摘On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].
基金This study was supported by grants from the National Natural Science Foundation of China(81972726,82273074 and 82372813)Dawn Project Foundation of Shanghai(21SG36)+2 种基金Shanghai Health Academic Leader Program(2022XD001)the Natural Science Foundation of Shanghai(22ZR1477900)Adjunct Talent Fund of Zhejiang Provincial People’s Hospital(2021-YT).
文摘Background:Cancer-related fatigue(CRF)is a common and debilitating symptom experienced by patients with advanced-stage cancer,especially those undergoing antitumor therapy.This study aimed to evaluate the efficacy and safety of Renshenguben(RSGB)oral solution,a ginseng-based traditional Chinese medicine,in alleviating CRF in patients with advanced hepatocellular carcinoma(HCC)receiving antitumor treatment.Methods:In this prospective,open-label,controlled,multicenter study,patients with advanced HCC at BCLC stage C and a brief fatigue inventory(BFI)score of≥4 were enrolled.Participants were assigned to the RSGB group(RSGB,10 mL twice daily)or the control group(with supportive care).Primary and secondary endpoints were the change in multidimensional fatigue inventory(MFI)score,and BFI and functional assessment of cancer therapy-hepatobiliary(FACT-Hep)scores at weeks 4 and 8 after enrollment.Adverse events(AEs)and toxicities were assessed.Results:A total of 409 participants were enrolled,with 206 assigned to the RSGB group.At week 4,there was a trend towards improvement,but the differences were not statistically significant.At week 8,the RSGB group exhibited a significantly lower MFI score(P<0.05)compared to the control group,indicating improved fatigue levels.Additionally,the RSGB group showed significantly greater decrease in BFI and FACT-Hep scores at week 8(P<0.05).Subgroup analyses among patients receiving various antitumor treatments showed similar results.Multivariate linear regression analyses revealed that the RSGB group experienced a significantly substantial decrease in MFI,BFI,and FACT-Hep scores at week 8.No serious drug-related AEs or toxicities were observed.Conclusions:RSGB oral solution effectively reduced CRF in patients with advanced HCC undergoing antitumor therapy over an eight-week period,with no discernible toxicities.These findings support the potential of RSGB oral solution as an adjunctive treatment for managing CRF in this patient population.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12161061)the Fundamental Research Funds for the Inner Mongolia University of Finance and Economics (Grant No. NCYWT23036)+2 种基金the Young Innovative and Entrepreneurial Talents of the Inner Mongolia Grassland Talents Project in 2022,Autonomous Region “Five Major Tasks” Research Special Project for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. NCXWD2422)High Quality Research Achievement Cultivation Fund for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. GZCG2426)the Talent Development Fund of Inner Mongolia Autonomous Region, China。
文摘Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.
基金the financial support provided by the National Natural Science Foundation of China(Grant No.42272310).
文摘Cyclic loads generated by environmental factors,such as winds,waves,and trains,will likely lead to performance degradation in pile foundations,resulting in issues like permanent displacement accumulation and bearing capacity attenuation.This paper presents a semi-analytical solution for predicting the axial cyclic behavior of piles in sands.The solution relies on two enhanced nonlinear load-transfer models considering stress-strain hysteresis and cyclic degradation in the pile-soil interaction.Model parameters are calibrated through cyclic shear tests of the sand-steel interface and laboratory geotechnical testing of sands.A novel aspect involves the meticulous formulation of the shaft loadtransfer function using an interface constitutive model,which inherently inherits the interface model’s advantages,such as capturing hysteresis,hardening,degradation,and particle breakage.The semi-analytical solution is computed numerically using the matrix displacement method,and the calculated values are validated through model tests performed on non-displacement and displacement piles in sands.The results demonstrate that the predicted values show excellent agreement with the measured values for both the static and cyclic responses of piles in sands.The displacement pile response,including factors such as bearing capacity,mobilized shaft resistance,and convergence rate of permanent settlement,exhibit improvements compared to non-displacement piles attributed to the soil squeezing effect.This methodology presents an innovative analytical framework,allowing for integrating cyclic interface models into the theoretical investigation of pile responses.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
基金supported by the National Key R&D Program of China under Grant No.2022YFB3608400National Natural Science Foundation of China under Grant Nos.61825404,61888102,and 62104044the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB44000000 and the project of MOE innovation platform.
文摘The performance and reliability of ferroelectric thin films at temperatures around a few Kelvin are critical for their application in cryo-electronics.In this work,TiN/Hf_(0.5)Zr_(0.5)O_(2)/TiN capacitors that are free from the wake-up effect are investigated systematically from room temperature(300 K)to cryogenic temperature(30 K).We observe a consistent decrease in permittivity(εr)and a progressive increase in coercive electric field(Ec)as temperatures decrease.Our investigation reveals exceptional stability in the double remnant polarization(2P_(r))of our ferroelectric thin films across a wide temperature range.Specifically,at 30 K,a 2P_(r)of 36μC/cm^(2)under an applied electric field of 3.0 MV/cm is achieved.Moreover,we observed a reduced fatigue effect at 30 K in comparison to 300 K.The stable ferroelectric properties and endurance characteristics demonstrate the feasibility of utilizing HfO_(2)based ferroelectric thin films for cryo-electronics applications.
文摘In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.
基金LMP acknowledges financial support from ANID through Convocatoria Nacional Subvención a Instalación en la Academia Convocatoria Año 2021,Grant SA77210040。
文摘We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.
基金We would like to acknowledge all the reviewers and editors and the sponsorship of National Natural Science Foundation of China(42030103)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(2021QNLM020001-6)the Laoshan National Laboratory of Science and Technology Foundation(LSKJ202203400).
文摘Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.