An Analytical Solution for Advance of Solute Front in Soils

Based on the assumption that solute transport in a semi-infinite soil columnor in a field soil profile can be described by the boundary-layer method, an analytical solution ispresented for the advance of a solute front with time. The traditional convection-dispersionequation (CDE) subjected to two boundary conditions: 1) at the soil surface (or inlet boundary) and2) at the solute front, was solved using a Laplace transformation. A comparison of residentconcentrations using a boundary-layer method and an exact solution (in a semi-infinite-domain)showed that both were in good agreement within the range between the two boundaries. This led to anew method for estimating solute transport parameters in soils, requiring only observation ofadvance of the solute front with time. This may be corroborated visually using a tracer solutionwith marking-dye or measured utilizing time domain reflectometry (TDR). This method is applicable toboth laboratory soil columns and field soils. Thus, it could be a step forward for modeling solutetransport in field soils and for better understanding of the transport processes in soils.

Solute transport and geochemical modeling of the coastal quaternary aquifer, Delta Dahab Basin, South Sinai, Egypt

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.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

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.

Modeling impact of culture facilities on hydrodynamics and solute transport in marine aquaculture waters of North Yellow Sea

An increasing number of marine aquaculture facilities have been placed in shallow bays and open sea,which might significantly affect hydrodynamic and solute transport processes in marine aquaculture waters.In this study,a coupled hydrodynamic and solute transport model was developed with high-resolution schemes in marine aquaculture waters based on depth-averaged shallow water equations.A new expression of drag force was incorporated into the momentum equations to express the resistance of suspended culture cages.The coupled model was used to simulate the effect of suspended structures on tidal currents and the movement of a contaminant cloud in the marine aquaculture of the North Yellow Sea,China.The simulation results showed a low-velocity area appearing inside the aquaculture cage area,with a maximum reduction rate of velocity close to 45%under high-density culture.The results also showed that tidal currents were sensitive to the density of suspended cages,the length of cages,and the drag coefficients of cages.The transport processes of pollutants inside aquaculture facilities were inhibited away from the vicinity of the culture cage area because of the diminished tidal currents.Therefore,the suspended cages significantly affected the transport processes of pollutants in the coastal aquaculture waters.Furthermore,the reduced horizontal velocity significantly decreased the food supply for the aquaculture areas from the surrounding sea.

Solute drag-controlled grain growth in magnesium investigated by quasi in-situ orientation mapping and level-set simulations

Critical properties of metallic materials,such as the yield stress,corrosion resistance and ductility depend on the microstructure and its grain size and size distribution.Solute atoms that favorably segregate to grain boundaries produce a pinning atmosphere that exerts a drag pressure on the boundary motion,which strongly affects the grain growth behavior during annealing.In the current work,the characteristics of grain growth in an annealed Mg-1 wt.%Mn-1 wt.%Nd magnesium alloy were investigated by advanced experimental and modeling techniques.Systematic quasi in-situ orientation mappings with a scanning electron microscope were performed to track the evolution of local and global microstructural characteristics as a function of annealing time.Solute segregation at targeted grain boundaries was measured using three-dimensional atom probe tomography.Level-set computer simulations were carried with different setups of driving forces to explore their contribution to the microstructure development with and without solute drag.The results showed that the favorable growth advantage for some grains leading to a transient stage of abnormal grain growth is controlled by several drivers with varying importance at different stages of annealing.For longer annealing times,residual dislocation density gradients between large and smaller grains are no longer important,which leads to microstructure stability due to predominant solute drag.Local fluctuations in residual dislocation energy and solute concentration near grain boundaries cause different boundary segments to migrate at different rates,which affects the average growth rate of large grains and their evolved shape.

Solute carrier-related signature for assessing prognosis and immunity in patients with clear-cell renal cell carcinoma

Background:Clear-cell renal cell carcinoma(ccRCC)is the most common malignant kidney cancer.However,the tumor microenvironment and crosstalk involved in metabolic reprogramming in ccRCC are not well-understood.Methods:We used The Cancer Genome Atlas to obtain ccRCC transcriptome data and clinical information.The EMTAB-1980 cohort was used for external validation.The GENECARDS database contains the first 100 solute carrier(SLC)-related genes.The predictive value of SLC-related genes for ccRCC prognosis and treatment was assessed using univariate Cox regression analysis.An SLC-related predictive signature was developed through Lasso regression analysis and used to determine the risk profiles of patients with ccRCC.Patients in each cohort were separated into high-and low-risk groups based on their risk scores.The clinical importance of the signature was assessed through survival,immune microenvironment,drug sensitivity,and nomogram analyses using R software.Results:SLC25A23,SLC25A42,SLC5A1,SLC3A1,SLC25A37,SLC5A6,SLCO5A1,and SCP2 comprised the signatures of the eight SLCrelated genes.Patients with ccRCC were separated into high-and low-risk groups based on the risk value in the training and validation cohorts;the high-risk group had a significantly worse prognosis(p<0.001).The risk score was an independent predictive indicator of ccRCC in the two cohorts according to univariate and multivariate Cox regression(p<0.05).Analysis of the immune microenvironment showed that immune cell infiltration and immune checkpoint gene expression differed between the two groups(p<0.05).Drug sensitivity analysis showed that compared to the low-risk group,the high-risk group was more sensitive to sunitinib,nilotinib,JNK-inhibitor-VIII,dasatinib,bosutinib,and bortezomib(p<0.001).Survival analysis and receiver operating characteristic curves were validated using the E-MTAB-1980 cohort.Conclusions:SLC-related genes have predictive relevance in ccRCC and play roles in the immunological milieu.Our results provide insight into metabolic reprogramming in ccRCC and identify promising treatment targets for ccRCC.

Effect of Osmotic Stress with PEG6000 on Osmotic Adjustment Solute in Seedling Leaves of Chenopodium album L.

[ Objective] The purpose was to discuss drought resistance mechanism of Chenopodium album L. and supply theoretical basis and practical guidance for artificial cultivation and popularization of C. album. [ Method] C. album seedlings grown to 6th leaf stage were conducted osmotic stress treatment with PEG6000 osmotic whose concentration was set up as 0, 5%, 10% and 20% and the various physiological indices of the 3rd -5th function leaves in upper plant were determined after being treated for 0, 1,3, 5, 7 and 9 d. [ Result] Under osmotic stress with 5% PGE, the relative water content （RWC） of C. album reduced less. Under osmotic stress with 10%, the RWC in seedling leaves of C. album decreased to 62% on the fifth day and the leaves began to wither. Under osmotic stress with 20%, the RWC in seedling leaves of C. album decreased to 61.9% on the third day and the leaves appeared withering, and the RWC decreased to 48.6% on the 7th day and the leaves were dry and yellow. Proline contents in seedling leaves of C. album under osmotic stress with 5%, 10% and 20% PEG were 7.64, 10.9 and 29.4 times of CK on the 7th day. [ Conclusion] C. album hed some adaptability to moderate osmotic stress, but the PEG osmotic stress with high concentration and long time might lead to severe damage on C. album.

Effect of atomic structure on migration characteristic and solute segregation of ordered domain interfaces formed in Ni_(75)Al_xV_(25-x)

Based on the microscopic phase-field model, ordered domain interfaces formed between D022 （Ni3V） phases along [001] direction in Ni75AlxV25-x alloys were simulated, and the effects of atomic structure on the migration characteristic and solute segregation of interfaces were studied. It is found that the migration ability is related to the atomic structure of interfaces, and three kinds of interfaces can migrate except the interface （001）//（002） which has the characteristic of L12 （Ni3Al） structure. V atoms jump to the nearest neighbor site and substitute for Ni, and vice versa. Because of the site selectivity behaviors of jumping atoms, the number of jumping atoms during the migration is the least and the jumping distance of atoms is the shortest among all possible modes, and the atomic structures of interfaces are unchanged before and after the migration. The preferences and degree of segregation or depletion of alloy elements are also related to the atomic structure of interface.

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

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.

Equilibrium Swelling and Solute Diffusion Characteristics of Poly (Methacrylic Acid co-Poloxamer) Hydrogels

Poly(methacrylic acid co-poloxamer) hydrogel networks were synthesized by free radical solution polymerization and their equilibrium swelling and solute permeation properties were characterized. These gels exhibited pH dependant swelling and solute diffusivity due to the formation or disruption of hydrogen bonded complexation between methacrylic acid (MAA) and etheric (EO). In neutral and basic conditions (above the swelling transition pH), the copolymer swelling was greatly higher than acid condition. In complexed hydrogels, the diffusion coefficients of vitamin B12 (VB12) were in the range of 10-10 to 10-7 cm2s-1; While in uncomplexed hydrogels, the values were about 210-6 cm2s-1. The comonomer composition and synthesis conditions have great effect on the structure, and thereby, swelling and solute diffusion characteristics of the resultant hydrogels. For the copolymers with composition of less than or more than 1:1 MAA/EO molar ratio, the plot of lnD vs 1/H-1 followed two different linear equations of 慺ree volume theory? respectively.

Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

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.

Smart prediction of liquefaction-induced lateral spreading

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.

Recent advancements in thermal conductivity of magnesium alloys

As highly integrated circuits continue to advance,accompanied by a growing demand for energy efficiency and weight reduction,materials are confronted with mounting challenges pertaining to thermal conductivity and lightweight properties.By virtue of numerous intrinsic mechanisms,as a result,the thermal conductivity and mechanical properties of the Mg alloys are often inversely related,which becomes a bottleneck limiting the application of Mg alloys.Based on several effective modification methods to improve the thermal conductivity of Mg alloys,this paper describes the law of how they affect the mechanical properties,and clearly indicates that peak aging treatment is one of the best ways to simultaneously enhance an alloy's thermal conductivity and mechanical properties.As the most frequently used Mg alloy,cast alloys exhibit substantial potential for achieving high thermal conductivity.Moreover,recent reports indicate that hot deformation can significantly improve the mechanical properties while maintaining,and potentially slightly enhancing,the alloy's thermal conductivity.This presents a meaningful way to develop Mg alloys for applications in the field of small-volume heat dissipation components that require high strength.This comprehensive review begins by outlining standard testing and prediction methods,followed by the theoretical models used to predict thermal conductivity,and then explores the primary influencing factors affecting thermal conductivity.The review summarizes the current development status of Mg alloys,focusing on the quest for alloys that offer both high thermal conductivity and high strength.It concludes by providing insights into forthcoming prospects and challenges within this field.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

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.

PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

Solution approximations for a mathematical model of relativistic electrons with beta derivative

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

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.

THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE

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.

Pumping-induced Well Hydraulics and Groundwater Budget in a Leaky Aquifer System with Vertical Heterogeneity in Aquitard Hydraulic Properties

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.

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

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.