This work aims at the mathematical modeling of a parabolic trough concentrator, the numerical resolution of the resulting equation, as well as the simulation of the heat transfer fluid heating process. To do this, a t...This work aims at the mathematical modeling of a parabolic trough concentrator, the numerical resolution of the resulting equation, as well as the simulation of the heat transfer fluid heating process. To do this, a thermal balance was established for the heat transfer fluid, the absorber and the glass. This allowed us to establish an equation system whose resolution was done by the finite difference method. Then, a computer program was developed to simulate the temperatures of the heat transfer fluid, the absorber tube and the glass as a function of time and space. The numerical resolution made it possible to obtain the temperatures of the heat transfer fluid, the absorber and the glass. The simulation of the fluid heating process was done in one-hour time steps, from six in the morning to six in the afternoon. The results obtained show that the temperature difference between the inlet and the outlet of the sensor is very significant. These results obtained, regarding the variation of the temperatures of the heat transfer fluid, the absorber and the glass, as well as the powers and efficiency of the parabolic trough concentrator and various factors, allow for the improvement of the performances of our prototype.展开更多
The effects of the Rashba spin–orbit interaction and external electric and magnetic fields on the thermodynamic properties of parabolic quantum dots are investigated.An explicit partition function is derived,and ther...The effects of the Rashba spin–orbit interaction and external electric and magnetic fields on the thermodynamic properties of parabolic quantum dots are investigated.An explicit partition function is derived,and thermodynamic quantities,including specific heat,entropy,and magnetic susceptibility,are analyzed.The behavior of Shannon entropy-related thermodynamic quantities is examined under varying magnetic fields and Hamiltonian parameters through numerical analysis.The results reveal a pronounced Schottky anomaly in the heat capacity at lower temperatures.The susceptibility exhibits a progressive enhancement and transitions to higher values with changes in the quantum dot parameters.In the presence of the Rashba spin–orbit interaction,the specific heat increases with temperature,reaches a peak,and then decreases to zero.Additionally,the susceptibility increases with theβparameter for varying Rashba spin–orbit interaction coefficients,and at a fixed temperature,it further increases with the Rashba coefficient.展开更多
High-power laser systems have opened new frontiers in scientifi research and have revolutionized various scientifi fields offering unprecedented capabilities for understanding fundamental physics and allowing unique a...High-power laser systems have opened new frontiers in scientifi research and have revolutionized various scientifi fields offering unprecedented capabilities for understanding fundamental physics and allowing unique applications.This paper details the successful commissioning of the 1 PW experimental area at the Extreme Light Infrastructure–Nuclear Physics(ELI-NP)facility in Romania,using both of the available laser arms.The experimental setup featured a short focal parabolic mirror to accelerate protons through the target normal sheath acceleration mechanism.Detailed experiments were conducted using various metallic and diamond-like carbon targets to investigate the dependence of the proton acceleration on different laser parameters.Furthermore,the paper discusses the critical role of the laser temporal profil in optimizing proton acceleration,supported by hydrodynamic simulations that are correlated with experimental outcomes.The finding underscore the potential of the ELI-NP facility to advance research in laser–plasma physics and contribute significantl to high-energy physics applications.The results of this commissioning establish a strong foundation for experiments by future users.展开更多
In this paper,a class of semilinear parabolic equations with cross coupling of power and exponential functions and large initial values are studied.By constructing and solving ordinary differential equations,the upper...In this paper,a class of semilinear parabolic equations with cross coupling of power and exponential functions and large initial values are studied.By constructing and solving ordinary differential equations,the upper and lower bounds on the solution life span of the equations areobtained.展开更多
This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the beh...This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.展开更多
An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into ...An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.展开更多
A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the re...A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions.The conditions for the validity of this approximation are also discussed.Furthermore,a formula that incorporates waveguide effects for the modal group velocity is derived,revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes.The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions,but also provides a wider range of depth applicability.Additionally,this method exhibits strong agreement with numerical methods and offers valuable physical insights.Finally,the method is applied to the study of very-low-frequency sound propagation in the South China Sea,leading to sound transmission loss predictions that closely align with experimental observations.展开更多
Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton...Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.展开更多
Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak...Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak functions.On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions,a Poincar′e-type inequality,an integration-by-parts formula and a trace result.Bringing together these results,we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.展开更多
In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(...In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.展开更多
This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△...This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.展开更多
A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx...A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).展开更多
To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem...To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.展开更多
In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,...In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,t）＋h（x,t）u^p（x,t）=0（p 〉 1） on Riemannian manifolds.As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang （[1], Bull. London Math. Soc. 38（2006）, 1045-1053） and the author （[2], Nonlinear Anal. 74 （2011）, 5141-5146）.展开更多
In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples ar...In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.展开更多
The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron an...The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3 Ga0.7 AS parabolic quantum well structures are obtained as functions of the well width. It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.展开更多
This paper deals with the blow-up rate of positive solution for a semilinearparabolic system coupled in the equations and boundary condition. The upper and lower bounds ofblow-up rates are obtained.
This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic...This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic equations for the concentrations u（x, t） and v（x, t） with an unknown point source F（x, t） = A（ t）δ（x- s） related to the concentration u（x, t）, where s is the point source location and A（t） is the amplitude of the pollution point source. Assuming that source F becomes inactive after time T＊, it is proved that it can be uniquely determined by the indirect measurements { v（0, t）, v（ a, t）, v（ b, t）, v（ l, t）, 0 〈 t ≤ T, T＊ 〈 T}, and, thus, the local Lipschitz stability for this inverse source problem is obtained. Based on the proof of its uniqueness, an inversion scheme is presented to determine the point source. Finally, two numerical examples are given to show the feasibility of the inversion scheme.展开更多
Two dimensional parabolic stability equations (PSE) are numerically solved using expansions in orthogonal functions in the normal direction.The Chebyshev polynomials approximation,which is a very useful form of ortho...Two dimensional parabolic stability equations (PSE) are numerically solved using expansions in orthogonal functions in the normal direction.The Chebyshev polynomials approximation,which is a very useful form of orthogonal expansions, is applied to solving parabolic stability equations. It is shown that results of great accuracy are effectively obtained.The availability of using Chebyshev approximations in parabolic stability equations is confirmed.展开更多
文摘This work aims at the mathematical modeling of a parabolic trough concentrator, the numerical resolution of the resulting equation, as well as the simulation of the heat transfer fluid heating process. To do this, a thermal balance was established for the heat transfer fluid, the absorber and the glass. This allowed us to establish an equation system whose resolution was done by the finite difference method. Then, a computer program was developed to simulate the temperatures of the heat transfer fluid, the absorber tube and the glass as a function of time and space. The numerical resolution made it possible to obtain the temperatures of the heat transfer fluid, the absorber and the glass. The simulation of the fluid heating process was done in one-hour time steps, from six in the morning to six in the afternoon. The results obtained show that the temperature difference between the inlet and the outlet of the sensor is very significant. These results obtained, regarding the variation of the temperatures of the heat transfer fluid, the absorber and the glass, as well as the powers and efficiency of the parabolic trough concentrator and various factors, allow for the improvement of the performances of our prototype.
文摘The effects of the Rashba spin–orbit interaction and external electric and magnetic fields on the thermodynamic properties of parabolic quantum dots are investigated.An explicit partition function is derived,and thermodynamic quantities,including specific heat,entropy,and magnetic susceptibility,are analyzed.The behavior of Shannon entropy-related thermodynamic quantities is examined under varying magnetic fields and Hamiltonian parameters through numerical analysis.The results reveal a pronounced Schottky anomaly in the heat capacity at lower temperatures.The susceptibility exhibits a progressive enhancement and transitions to higher values with changes in the quantum dot parameters.In the presence of the Rashba spin–orbit interaction,the specific heat increases with temperature,reaches a peak,and then decreases to zero.Additionally,the susceptibility increases with theβparameter for varying Rashba spin–orbit interaction coefficients,and at a fixed temperature,it further increases with the Rashba coefficient.
基金supported by the Extreme Light Infrastructure–Nuclear Physics(ELI-NP)PhaseⅡa project co-finance by the Romanian Government and the European Union through the European Regional Development Fund,by the Romanian Ministry of Education and Research CNCS-UEFISCDI(Project No.PN-ⅡIP4-IDPCCF-2016-0164)+1 种基金Nucleu Projects(Grant No.PN 23210105 and 19060105)supports ELI-NP through IOSIN funds as a Facility of National Interest。
文摘High-power laser systems have opened new frontiers in scientifi research and have revolutionized various scientifi fields offering unprecedented capabilities for understanding fundamental physics and allowing unique applications.This paper details the successful commissioning of the 1 PW experimental area at the Extreme Light Infrastructure–Nuclear Physics(ELI-NP)facility in Romania,using both of the available laser arms.The experimental setup featured a short focal parabolic mirror to accelerate protons through the target normal sheath acceleration mechanism.Detailed experiments were conducted using various metallic and diamond-like carbon targets to investigate the dependence of the proton acceleration on different laser parameters.Furthermore,the paper discusses the critical role of the laser temporal profil in optimizing proton acceleration,supported by hydrodynamic simulations that are correlated with experimental outcomes.The finding underscore the potential of the ELI-NP facility to advance research in laser–plasma physics and contribute significantl to high-energy physics applications.The results of this commissioning establish a strong foundation for experiments by future users.
基金Supported by Key Project Funding for Shaanxi Higher Education Teaching Reform Research (23BZ078)Shaanxi Provincial Education Science Planning Project (SGH24Y2782)+4 种基金Shaanxi Provincial Social Science Foundation Program(2024D008)Key Projects of the Second Huang Yanpei Vocational Education Thought Research Planning Project (ZJS2024ZN026)Shaanxi Higher Education Society Key Projects(XGHZ2301)2024 Annual Planning Project of the China Association for Non-Government Education (School Development Category)(CANFZG24095)the Youth Innovation Team of Shaanxi Universities。
文摘In this paper,a class of semilinear parabolic equations with cross coupling of power and exponential functions and large initial values are studied.By constructing and solving ordinary differential equations,the upper and lower bounds on the solution life span of the equations areobtained.
基金Supported by Shandong Provincial Natural Science Foundation(Grant Nos.ZR2021MA003 and ZR2020MA020).
文摘This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12001210 and 12261103)the Natural Science Foundation of Henan(Grant No.252300420308)the Yunnan Fundamental Research Projects(Grant No.202301AT070117).
文摘An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12174048 and 12204128)。
文摘A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions.The conditions for the validity of this approximation are also discussed.Furthermore,a formula that incorporates waveguide effects for the modal group velocity is derived,revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes.The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions,but also provides a wider range of depth applicability.Additionally,this method exhibits strong agreement with numerical methods and offers valuable physical insights.Finally,the method is applied to the study of very-low-frequency sound propagation in the South China Sea,leading to sound transmission loss predictions that closely align with experimental observations.
文摘Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.
文摘Sciences and Technologies Team(ESTE),Abstract We consider nonlinear parabolic problems in a variational framework.The leading part is a monotone operator whose growth is controlled by time-and space-dependent Musielak functions.On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions,a Poincar′e-type inequality,an integration-by-parts formula and a trace result.Bringing together these results,we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.
文摘In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.
文摘This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.
文摘A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).
文摘To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.
基金supported by the National Science Foundation of China(41275063 and 11401575)
文摘In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,t）＋h（x,t）u^p（x,t）=0（p 〉 1） on Riemannian manifolds.As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang （[1], Bull. London Math. Soc. 38（2006）, 1045-1053） and the author （[2], Nonlinear Anal. 74 （2011）, 5141-5146）.
文摘In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.
文摘The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3 Ga0.7 AS parabolic quantum well structures are obtained as functions of the well width. It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.
文摘This paper deals with the blow-up rate of positive solution for a semilinearparabolic system coupled in the equations and boundary condition. The upper and lower bounds ofblow-up rates are obtained.
基金The National Natural Science Foundation of China(No.10861001)the Natural Science Foundation of Jiangxi Province
文摘This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic equations for the concentrations u（x, t） and v（x, t） with an unknown point source F（x, t） = A（ t）δ（x- s） related to the concentration u（x, t）, where s is the point source location and A（t） is the amplitude of the pollution point source. Assuming that source F becomes inactive after time T＊, it is proved that it can be uniquely determined by the indirect measurements { v（0, t）, v（ a, t）, v（ b, t）, v（ l, t）, 0 〈 t ≤ T, T＊ 〈 T}, and, thus, the local Lipschitz stability for this inverse source problem is obtained. Based on the proof of its uniqueness, an inversion scheme is presented to determine the point source. Finally, two numerical examples are given to show the feasibility of the inversion scheme.
文摘Two dimensional parabolic stability equations (PSE) are numerically solved using expansions in orthogonal functions in the normal direction.The Chebyshev polynomials approximation,which is a very useful form of orthogonal expansions, is applied to solving parabolic stability equations. It is shown that results of great accuracy are effectively obtained.The availability of using Chebyshev approximations in parabolic stability equations is confirmed.
