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GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY 被引量:1
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作者 丁时进 李颖花 王喻 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期195-214,共20页
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
关键词 Navier-Stokes/Allen-Cahn system density-dependent viscosity free boundary global solutions
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Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation
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作者 巩乾坤 王惠 王云虎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期409-416,共8页
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
关键词 lump solution rogue wave solution breather wave solution (2+1)-dimensional Hirota-Satsuma-Ito equation
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PDE Standardization Analysis and Solution of TypicalMechanics Problems
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作者 Ningjie Wang Yihao Wang +1 位作者 Yongle Pei Luxian Li 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期171-186,共16页
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 throu... 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. 展开更多
关键词 Three standard forms expression input PDE module deflection solution stress solution
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THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE
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作者 金可 石影 谢华飞 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期583-608,共26页
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
关键词 Schrödinger system ground states solutions bound state solutions
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Solution approximations for a mathematical model of relativistic electrons with beta derivative
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作者 Ibrahim Yalcinkaya Orkun Tasbozan +1 位作者 Ali Kurt Hijaz Ahmad 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期469-485,共17页
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... 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. 展开更多
关键词 Klein-Fock-Gordon(KFG)equation beta derivative semi-analytical solution exact solution
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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation BIFURCATIONS Phase Portrait Analytical Periodic Wave solution Periodic Cusp Wave solution
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Analytic Solutions for Hindered Rotation Quantum Problem
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作者 Mirco Ragni 《Applied Mathematics》 2024年第10期709-718,共10页
Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematic... Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematical advance in the description of physical phenomena described by the second derivative operator associated with a divergent interaction potential and, being analytical, guarantee the optimal interpretation of such phenomena. 展开更多
关键词 Analytics solutions Schrodinger Equation Interaction Potential
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Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition
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作者 Mohamed Karimou Gazibo Duni Yegbonoma Frédéric Zongo 《Applied Mathematics》 2024年第7期455-463,共9页
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
关键词 Lebesgue and Sobolev Spaces with Variable Exponent Weak solution Entropy solution Degenerate Parabolic-Hyperbolic Equation Conservation Law Leray Lions Type Operator Neumann Boundary Condition Existence Result
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Malargüe Site Remediation:A Successful Solution for Uranium Mill Tailings
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作者 BARARI E DíAZ J G +1 位作者 GIOMIA KEMPF R A 《原子能科学技术》 EI CAS CSCD 北大核心 2024年第10期2088-2094,共7页
Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with ... Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with its legal responsibilities,decides to implement a restoration project for all sites related to the mining and processing of uranium ores.The Malargüe Site is located within the Province of Mendoza in the city of Malargüe.It is the first site to successfully complete its remediation.The activities consist of relocation of tailings to an engineering repository.The tailings management(encapsulation) and rehabilitation of the area was finished in June 2017.The remediation alternative for the ore tailings was selected after conducting comparative studies and submitted the project to the society for consideration.The objective of the encapsulation of the mineral tails is to isolate them from the environment,also proceeding with the decontamination and rehabilitation of the area (landscaping,post-closure monitoring and 20 years monitoring period).Encapsulation consisted of the construction of a containment cell for the mine tailings,to isolate them and prevent pollutants from entering the environment through the transfer routes.To clean the impacted areas,the soil was removed,it was incorporated into the encapsulation,and the filling was carried out with natural soils from the area.Remediation prevents radon transfer to the environment,as ^(222)Ra is an alpha emitter with a half-life of four days,which produces its own radioactive progeny.Radon progeny are solids,and when a ^(222)Ra nucleus emits an alpha particle into the air,the resulting ^(218)Po nucleus,momentarily electrically charged,adheres to any dust particle.Remediation prevents the discharge into the air containing radon and also containing dust particles charged with intensely radioactive radon progeny.The tasks mentioned make it possible to decrease radon emanation,reduce radiological risks to the public and prevent the entry of rainwater into the system.In addition,the containment system prevents the discharge of contaminated liquids into the environment,avoiding contamination of the groundwater.All these activities are according to the concepts of sustainability. 展开更多
关键词 REMEDIATION radionuclide transfer TAILINGS ENCAPSULATION solution sustainable
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GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE
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作者 王晓闪 王忠谦 贾哲 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期909-924,共16页
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
关键词 global weak solutions attraction-repulsion P-LAPLACIAN logistic source
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Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions
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作者 孙志强 侯国林 +1 位作者 乔艳芬 刘金存 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第1期581-590,共10页
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
关键词 Hamiltonian system symplectic elasticity QUASICRYSTALS analytic solution state function
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On entire solutions of some Fermat type differential-difference equations
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作者 LONG Jian-ren QIN Da-zhuan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期69-88,共20页
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
关键词 entire solutions differential-difference equations EXISTENCE finite order
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Enhancing Cybersecurity through Cloud Computing Solutions in the United States
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作者 Omolola F. Hassan Folorunsho O. Fatai +4 位作者 Oluwadare Aderibigbe Abdullah Oladoyin Akinde Tolulope Onasanya Mariam Adetoun Sanusi Oduwunmi Odukoya 《Intelligent Information Management》 2024年第4期176-193,共18页
This study investigates how cybersecurity can be enhanced through cloud computing solutions in the United States. The motive for this study is due to the rampant loss of data, breaches, and unauthorized access of inte... This study investigates how cybersecurity can be enhanced through cloud computing solutions in the United States. The motive for this study is due to the rampant loss of data, breaches, and unauthorized access of internet criminals in the United States. The study adopted a survey research design, collecting data from 890 cloud professionals with relevant knowledge of cybersecurity and cloud computing. A machine learning approach was adopted, specifically a random forest classifier, an ensemble, and a decision tree model. Out of the features in the data, ten important features were selected using random forest feature importance, which helps to achieve the objective of the study. The study’s purpose is to enable organizations to develop suitable techniques to prevent cybercrime using random forest predictions as they relate to cloud services in the United States. The effectiveness of the models used is evaluated by utilizing validation matrices that include recall values, accuracy, and precision, in addition to F1 scores and confusion matrices. Based on evaluation scores (accuracy, precision, recall, and F1 scores) of 81.9%, 82.6%, and 82.1%, the results demonstrated the effectiveness of the random forest model. It showed the importance of machine learning algorithms in preventing cybercrime and boosting security in the cloud environment. It recommends that other machine learning models be adopted to see how to improve cybersecurity through cloud computing. 展开更多
关键词 CYBERSECURITY Cloud Computing Cloud solutions Machine Learning Algorithm
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Effect of inorganic salt impurities on seeded precipitation of silica hydrate from sodium silicate solution
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作者 Xiao-bin LI Xiao-bing GAO +5 位作者 Qiu-sheng ZHOU Yi-lin WANG Tian-gui QI Lei-ting SHEN Gui-hua LIU Zhi-hong PENG 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2024年第9期3016-3028,共13页
To clarify the precipitation of silica hydrate from the real desilication solutions of aluminosilicate solid wastes by adding seeds and improve integrated waste utilization,the seeded precipitation was studied using s... To clarify the precipitation of silica hydrate from the real desilication solutions of aluminosilicate solid wastes by adding seeds and improve integrated waste utilization,the seeded precipitation was studied using synthesized sodium silicate solution containing different inorganic salt impurities.The results show that sodium chloride,sodium sulfate,sodium carbonate,or calcium chloride can change the siloxy group structure.The number of high-polymeric siloxy groups decreases with increasing sodium chloride or sodium sulfate concentration,which is detrimental to seeded precipitation.Calcium chloride favors the polymerization of silicate ions,and even the chain groups precipitate with the precipitation of high-polymeric sheet and cage-like siloxy groups.The introduced sodium cations in sodium carbonate render a more open network structure of high-polymeric siloxy groups,although the carbonate ions favor the polymerization of siloxy groups.No matter how the four impurities affect the siloxy group structure,the precipitates are always amorphous opal-A silica hydrate. 展开更多
关键词 ALUMINOSILICATE sodium silicate solution siloxy group IMPURITY silica hydrate
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ON THE STABILITY OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC DIFFERENTIAL EQUATIONS
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作者 Maoan HAN Yan YE 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1524-1535,共12页
In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol... In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications. 展开更多
关键词 periodic solution Poincarémap periodic equation stability
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Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers
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作者 兰中周 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第6期119-123,共5页
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
关键词 complex modified KdV equation multi-soliton solutions breather-like BOUND-STATE
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A COMPACT EMBEDDING RESULT FOR NONLOCAL SOBOLEV SPACES AND MULTIPLICITY OF SIGN-CHANGING SOLUTIONS FOR NONLOCAL SCHRÖDINGER EQUATIONS
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作者 Xu ZHANG Hao ZHAI Fukun ZHAO 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1853-1876,共24页
For any s∈(0,1),let the nonlocal Sobolev space X^(s)(ℝ^(N))be the linear space of Lebesgue measure functions fromℝN toℝsuch that any function u in X^(s)(ℝ^(N))belongs to L2(ℝN)and the function(x,y)\longmapsto\big(u(x... For any s∈(0,1),let the nonlocal Sobolev space X^(s)(ℝ^(N))be the linear space of Lebesgue measure functions fromℝN toℝsuch that any function u in X^(s)(ℝ^(N))belongs to L2(ℝN)and the function(x,y)\longmapsto\big(u(x)-u(y)\big)\sqrt{K(x-y)}is in L2(ℝN,ℝN).First,we show,for a coercive function V(x),the subspace E:=\bigg\{u\in X^s(\mathbb{R}^N):\int_{\mathbb{R}^N}V(x)u^2{\rm d}x<+\infty\bigg\}of X^(s)(ℝ^(N))is embedded compactly into L^(p)(ℝ^(N))for p\in[2,2_s^*),where 2_s^*is the fractional Sobolev critical exponent.In terms of applications,the existence of a least energy sign-changing solution and infinitely many sign-changing solutions of the nonlocal Schrödinger equation-{\cal{L}_K}u+V(x)u=f(x,u),\x\in\\mathbb{R}^N are obtained,where-{\cal{L}_K}is an integro-differential operator and V is coercive at infinity. 展开更多
关键词 sign-changing solution integro-differential operator least energy variational method
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Investigation of Cavitation in NaCl Solutions in a Sonochemical Reactor Using the Foil Test Method
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作者 Michael Kuchinskiy Tatyana Lyubimova +2 位作者 Konstantin Rybkin Anastasiia Sadovnikova Vasiliy Galishevskiy 《Fluid Dynamics & Materials Processing》 EI 2024年第5期1093-1102,共10页
Ultrasonic baths and sonochemical reactors are widely used in industrial applications dealing with surface cleaningand chemical synthesis. The processes of erosion, cleaning and structuring of the surface can be typic... Ultrasonic baths and sonochemical reactors are widely used in industrial applications dealing with surface cleaningand chemical synthesis. The processes of erosion, cleaning and structuring of the surface can be typically controlledby changing relevant influential parameters. In particular, in this work, we experimentally investigate theeffect of NaCl concentration (0–5.5 mol/L) on the erosion of an aluminum foil under ultrasonic exposure at afrequency of 28 kHz. Special attention is paid to the determination of cavitation zones and their visualizationusing heat maps. It is found that at low NaCl concentration (0.3 mol/L), the foil destruction rate is higher thanin distilled water. At higher concentrations of salt, cavitation takes place mainly in the upper part of the container. 展开更多
关键词 ULTRASOUND NaCl solution foil test cavitation activity
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Bifurcation Analysis Reveals Solution Structures of Phase Field Models
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作者 Xinyue Evelyn Zhao Long-Qing Chen +1 位作者 Wenrui Hao Yanxiang Zhao 《Communications on Applied Mathematics and Computation》 EI 2024年第1期64-89,共26页
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifur... The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method. 展开更多
关键词 Phase field modeling BIFURCATIONS Multiple solutions
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Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media
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作者 Pan Huang Yifei Leng +1 位作者 Cheng Lian Honglai Liu 《Engineering》 SCIE EI CAS CSCD 2024年第8期94-103,共10页
Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varyi... Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media. 展开更多
关键词 Porous media Reactive transport solution operator DeepONet Neural network
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