： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati tech...： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The resu...By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The results in this paper unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. The Theorems in this paper are new even in the continuous and the discrete cases.展开更多
Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equa...Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.展开更多
Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend...Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. At the end of this paper, we give an example to illustrate the main results.展开更多
In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe...In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.展开更多
Gas turbines play core roles in clean energy supply and the construction of comprehensive energy systems.The control performance of primary frequency modulation of gas turbines has a great impact on the frequency cont...Gas turbines play core roles in clean energy supply and the construction of comprehensive energy systems.The control performance of primary frequency modulation of gas turbines has a great impact on the frequency control of the power grid.However,there are some control difficulties in the primary frequency modulation control of gas turbines,such as the coupling effect of the fuel control loop and speed control loop,slow tracking speed,and so on.To relieve the abovementioned difficulties,a control strategy based on the desired dynamic equation proportional integral(DDE-PI)is proposed in this paper.Based on the parameter stability region,a parameter tuning procedure is summarized.Simulation is carried out to address the ease of use and simplicity of the proposed tuning method.Finally,DDE-PI is applied to the primary frequency modulation system of an MS6001B heavy-duty gas turbine.The simulation results indicate that the gas turbine with the proposed strategy can obtain the best control performance with a strong ability to deal with system uncertainties.The proposed method shows good engineering application potential.展开更多
This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback att...This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.展开更多
The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple ba...The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.展开更多
Zeroing neural dynamic(ZND)model is widely deployed for time-variant non-linear equations(TVNE).Various element-wise non-linear activation functions and integration operations are investigated to enhance the convergen...Zeroing neural dynamic(ZND)model is widely deployed for time-variant non-linear equations(TVNE).Various element-wise non-linear activation functions and integration operations are investigated to enhance the convergence performance and robustness in most proposed ZND models for solving TVNE,leading to a huge cost of hardware implementation and model complexity.To overcome these problems,the authors develop a new norm-based ZND(NBZND)model with strong robustness for solving TVNE,not applying element-wise non-linear activated functions but introducing a two-norm operation to achieve finite-time convergence.Moreover,the authors develop a discretetime NBZND model for the potential deployment of the model on digital computers.Rigorous theoretical analysis for the NBZND is provided.Simulation results substantiate the advantages of the NBZND model for solving TVNE.展开更多
In this work,fow behavior and dynamic recrystallization(DRX)mechanism of a low carbon martensitic stainless bearing steel,CSS-42L,were investigated using a thermomechanical simulator under the temperature and strain r...In this work,fow behavior and dynamic recrystallization(DRX)mechanism of a low carbon martensitic stainless bearing steel,CSS-42L,were investigated using a thermomechanical simulator under the temperature and strain rate ranges of 900 to 1100℃ and 0.1 to 20 s^(−1),respectively.The Arrhenius-type constitutive equation was established based on the fow stress curves.Moreover,the peak stress decreased with the increase in deformation temperature and the decrease in strain rate.There were two DRX mechanisms during hot deformation of the current studied steel,the main one being discontinuous dynamic recrystallization mechanism,acting through grain boundary bulging and migration,and the auxiliary one being continuous dynamic recrystallization mechanism,working through the rotation of sub-grains.On the basis of microstructural characterizations,power dissipation maps and fow instability maps,the optimized hot deformation parameters for CSS-42L bearing steel were determined as 1050℃/0.1 s^(−1) and 1100℃/1 s^(−1).展开更多
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato...In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.展开更多
Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump coll...Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump collisions,and evolution behavior of multi-breathers.Firstly,the N-soliton solution of Ito equation is studied,and some high-order breather waves can be obtained from the N-soliton solutions through paired-complexification of parameters.Secondly,the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method,and the motion velocity and trajectory equations of high-order lump waves are analyzed.Moreover,based on the trajectory equations of the higher-order lump solutions,we give and prove the trajectory theorem of 1-lump before and after interaction with nsoliton.Finally,we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method.Meanwhile,some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.展开更多
This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and...This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and cost functional depend on the joint distribution of the state and the control.In our game,both the(lower and upper)value functions and the(lower and upper)second-order Bellman–Isaacs equations are defined on the Wasserstein space P_(2)(R^(n))which is an infinite dimensional space.The dynamic programming principle for the value functions is proved.If the(upper and lower)value functions are smooth enough,we show that they are the classical solutions to the second-order Bellman–Isaacs equations.On the other hand,the classical solutions to the(upper and lower)Bellman–Isaacs equations are unique and coincide with the(upper and lower)value functions.As an illustrative application,the linear quadratic case is considered.Under the Isaacs condition,the explicit expressions of optimal closed-loop controls for both players are given.Finally,we introduce the intrinsic notion of viscosity solution of our second-order Bellman–Isaacs equations,and characterize the(upper and lower)value functions as their viscosity solutions.展开更多
Liquid hydrogen has attracted much attention due to its high energy storage density and suitability for long-distance transportation.An efficient hydrogen liquefaction process is the key to obtaining liquid hydrogen.I...Liquid hydrogen has attracted much attention due to its high energy storage density and suitability for long-distance transportation.An efficient hydrogen liquefaction process is the key to obtaining liquid hydrogen.In an effort to determine the parameter optimization of the hydrogen liquefaction process,this paper employed process simulation software Aspen HYSYS to simulate the hydrogen liquefaction process.By establishing a dynamic model of the unit module,this study carried out dynamic simulation optimization based on the steady-state process and process parameters of the hydrogen liquefaction process and analyzed the dynamic characteristics of the process.Based on the pressure drop characteristic experiment,an equation for the pressure drop in the heat exchanger was proposed.The heat transfer of hydrogen conversion was simulated and analyzed,and its accuracy was verified by comparison with the literature.The dynamic simulation of a plate-fin heat exchanger was carried out by coupling heat transfer simulation and the pressure drop experiment.The results show that the increase in inlet temperature(5℃and 10℃)leads to an increase in specific energy consumption(0.65%and 1.29%,respectively)and a decrease in hydrogen liquefaction rate(0.63%and 2.88%,respectively).When the inlet pressure decreases by 28.57%,the hydrogen temperature of the whole liquefaction process decreases and the specific energy consumption increases by 52.94%.The research results are of great significance for improving the operating efficiency of the refrigeration cycle and guiding the actual liquid hydrogen production.展开更多
This paper introduces dynamic mode decomposition(DMD)as a novel approach to model the breakage kinetics of particulate systems.DMD provides a data-driven framework to identify a best-fit linear dynamics model from a s...This paper introduces dynamic mode decomposition(DMD)as a novel approach to model the breakage kinetics of particulate systems.DMD provides a data-driven framework to identify a best-fit linear dynamics model from a sequence of system measurement snapshots,bypassing the nontrivial task of determining appropriate mathemat-ical forms for the breakage kernel functions.A key innovation of our method is the instilling of physics-informed constraints into the DMD eigenmodes and eigenvalues,ensuring they adhere to the physical structure of particle breakage processes even under sparse measurement data.The integration of eigen-constraints is computationally aided by a zeroth-order global optimizer for solving the nonlinear,nonconvex optimization problem that elicits system dynamics from data.Our method is evaluated against the state-of-the-art optimized DMD algorithm using both generated data and real-world data of a batch grinding mill,showcasing over an order of magnitude lower prediction errors in data reconstruction and forecasting.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
This paper explores the rich structure of peakon and pseudo-peakon solutions for a class of higher-order b-family equations,referred to as the J-th b-family(J-bF)equations.We propose several conjectures concerning the...This paper explores the rich structure of peakon and pseudo-peakon solutions for a class of higher-order b-family equations,referred to as the J-th b-family(J-bF)equations.We propose several conjectures concerning the weak solutions of these equations,including a b-independent pseudo-peakon solution,a b-independent peakon solution,and a b-dependent peakon solution.These conjectures are analytically verified for J≤14 and/or J≤9 using the symbolic computation system MAPLE,which includes a built-in definition of the higher-order derivatives of the sign function.The b-independent pseudo-peakon solution is a 3rd-order pseudo-peakon for general arbitrary constants,with higher-order pseudo-peakons derived under specific parameter constraints.Additionally,we identify both b-independent and b-dependent peakon solutions,highlighting their distinct properties and the nuanced relationship between the parameters b and J.The existence of these solutions underscores the rich dynamical structure of the J-bF equations and generalizes previous results for lower-order equations.Future research directions include higher-order generalizations,rigorous proofs of the conjectures,interactions between different types of peakons and pseudo-peakons,stability analysis,and potential physical applications.These advancements significantly contribute to the understanding of peakon systems and their broader implications in mathematics and physics.展开更多
Semisubmersible naval ships are versatile military crafts that combine the advantageous features of high-speed planing crafts and submarines.At-surface,these ships are designed to provide sufficient speed and maneuver...Semisubmersible naval ships are versatile military crafts that combine the advantageous features of high-speed planing crafts and submarines.At-surface,these ships are designed to provide sufficient speed and maneuverability.Additionally,they can perform shallow dives,offering low visual and acoustic detectability.Therefore,the hydrodynamic design of a semisubmersible naval ship should address at-surface and submerged conditions.In this study,Numerical analyses were performed using a semisubmersible hull form to analyze its hydrodynamic features,including resistance,powering,and maneuvering.The simulations were conducted with Star CCM+version 2302,a commercial package program that solves URANS equations using the SST k-ωturbulence model.The flow analysis was divided into two parts:at-surface simulations and shallowly submerged simulations.At-surface simulations cover the resistance,powering,trim,and sinkage at transition and planing regimes,with corresponding Froude numbers ranging from 0.42 to 1.69.Shallowly submerged simulations were performed at seven different submergence depths,ranging from D/LOA=0.0635 to D/LOA=0.635,and at two different speeds with Froude numbers of 0.21 and 0.33.The behaviors of the hydrodynamic forces and pitching moment for different operation depths were comprehensively analyzed.The results of the numerical analyses provide valuable insights into the hydrodynamic performance of semisubmersible naval ships,highlighting the critical factors influencing their resistance,powering,and maneuvering capabilities in both at-surface and submerged conditions.展开更多
In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A...In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.展开更多
Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop ...Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.展开更多
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.
文摘By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The results in this paper unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. The Theorems in this paper are new even in the continuous and the discrete cases.
基金Supported by National Natural Science Foundation of China (10671069)
文摘Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.
文摘Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. At the end of this paper, we give an example to illustrate the main results.
基金supported by the National Natural Science Foundation of China(12071491,12001113)。
文摘In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.
基金supported by Science and Technology Project of Jiangsu Frontier Electric Technology Co.,Ltd. (Grant Number KJ202004),Gao A.M. (author who received the grant).
文摘Gas turbines play core roles in clean energy supply and the construction of comprehensive energy systems.The control performance of primary frequency modulation of gas turbines has a great impact on the frequency control of the power grid.However,there are some control difficulties in the primary frequency modulation control of gas turbines,such as the coupling effect of the fuel control loop and speed control loop,slow tracking speed,and so on.To relieve the abovementioned difficulties,a control strategy based on the desired dynamic equation proportional integral(DDE-PI)is proposed in this paper.Based on the parameter stability region,a parameter tuning procedure is summarized.Simulation is carried out to address the ease of use and simplicity of the proposed tuning method.Finally,DDE-PI is applied to the primary frequency modulation system of an MS6001B heavy-duty gas turbine.The simulation results indicate that the gas turbine with the proposed strategy can obtain the best control performance with a strong ability to deal with system uncertainties.The proposed method shows good engineering application potential.
文摘This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.
文摘The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.
基金Natural Science Foundation of China,Grant/Award Number:62206109Guangdong Basic and Applied Basic Research Foundation,Grant/Award Number:2022A1515010976+1 种基金Young Scholar Program of Pazhou Lab,Grant/Award Number:PZL2021KF0022National College Student Innovation and Entrepreneurship Training Program,Grant/Award Number:202410559070。
文摘Zeroing neural dynamic(ZND)model is widely deployed for time-variant non-linear equations(TVNE).Various element-wise non-linear activation functions and integration operations are investigated to enhance the convergence performance and robustness in most proposed ZND models for solving TVNE,leading to a huge cost of hardware implementation and model complexity.To overcome these problems,the authors develop a new norm-based ZND(NBZND)model with strong robustness for solving TVNE,not applying element-wise non-linear activated functions but introducing a two-norm operation to achieve finite-time convergence.Moreover,the authors develop a discretetime NBZND model for the potential deployment of the model on digital computers.Rigorous theoretical analysis for the NBZND is provided.Simulation results substantiate the advantages of the NBZND model for solving TVNE.
基金fnancially supported by the Scientifc Research Project of the Department of Education in Hunan Prov ince,China(Grant No.23B0533).
文摘In this work,fow behavior and dynamic recrystallization(DRX)mechanism of a low carbon martensitic stainless bearing steel,CSS-42L,were investigated using a thermomechanical simulator under the temperature and strain rate ranges of 900 to 1100℃ and 0.1 to 20 s^(−1),respectively.The Arrhenius-type constitutive equation was established based on the fow stress curves.Moreover,the peak stress decreased with the increase in deformation temperature and the decrease in strain rate.There were two DRX mechanisms during hot deformation of the current studied steel,the main one being discontinuous dynamic recrystallization mechanism,acting through grain boundary bulging and migration,and the auxiliary one being continuous dynamic recrystallization mechanism,working through the rotation of sub-grains.On the basis of microstructural characterizations,power dissipation maps and fow instability maps,the optimized hot deformation parameters for CSS-42L bearing steel were determined as 1050℃/0.1 s^(−1) and 1100℃/1 s^(−1).
文摘In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.
基金Project supported by the National Natural Science Foundation of China(Grant No.12461047)the Scientific Research Project of the Hunan Education Department(Grant No.24B0478).
文摘Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump collisions,and evolution behavior of multi-breathers.Firstly,the N-soliton solution of Ito equation is studied,and some high-order breather waves can be obtained from the N-soliton solutions through paired-complexification of parameters.Secondly,the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method,and the motion velocity and trajectory equations of high-order lump waves are analyzed.Moreover,based on the trajectory equations of the higher-order lump solutions,we give and prove the trajectory theorem of 1-lump before and after interaction with nsoliton.Finally,we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method.Meanwhile,some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.
基金supported by Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA032,ZR2022MA029)National Natural Science Foundation of China(Grant Nos.12171279,72171133)+1 种基金The second named author was supported by National Key R&D Program of China(Grant No.2022YFA1006102)National Natural Science Foundation of China(Grant No.11831010)。
文摘This paper concerns two-player zero-sum stochastic differential games with nonanticipative strategies against closed-loop controls in the case where the coefficients of mean-field stochastic differential equations and cost functional depend on the joint distribution of the state and the control.In our game,both the(lower and upper)value functions and the(lower and upper)second-order Bellman–Isaacs equations are defined on the Wasserstein space P_(2)(R^(n))which is an infinite dimensional space.The dynamic programming principle for the value functions is proved.If the(upper and lower)value functions are smooth enough,we show that they are the classical solutions to the second-order Bellman–Isaacs equations.On the other hand,the classical solutions to the(upper and lower)Bellman–Isaacs equations are unique and coincide with the(upper and lower)value functions.As an illustrative application,the linear quadratic case is considered.Under the Isaacs condition,the explicit expressions of optimal closed-loop controls for both players are given.Finally,we introduce the intrinsic notion of viscosity solution of our second-order Bellman–Isaacs equations,and characterize the(upper and lower)value functions as their viscosity solutions.
基金supported by the National Natural Science Foundation of China,China(No.52474088).
文摘Liquid hydrogen has attracted much attention due to its high energy storage density and suitability for long-distance transportation.An efficient hydrogen liquefaction process is the key to obtaining liquid hydrogen.In an effort to determine the parameter optimization of the hydrogen liquefaction process,this paper employed process simulation software Aspen HYSYS to simulate the hydrogen liquefaction process.By establishing a dynamic model of the unit module,this study carried out dynamic simulation optimization based on the steady-state process and process parameters of the hydrogen liquefaction process and analyzed the dynamic characteristics of the process.Based on the pressure drop characteristic experiment,an equation for the pressure drop in the heat exchanger was proposed.The heat transfer of hydrogen conversion was simulated and analyzed,and its accuracy was verified by comparison with the literature.The dynamic simulation of a plate-fin heat exchanger was carried out by coupling heat transfer simulation and the pressure drop experiment.The results show that the increase in inlet temperature(5℃and 10℃)leads to an increase in specific energy consumption(0.65%and 1.29%,respectively)and a decrease in hydrogen liquefaction rate(0.63%and 2.88%,respectively).When the inlet pressure decreases by 28.57%,the hydrogen temperature of the whole liquefaction process decreases and the specific energy consumption increases by 52.94%.The research results are of great significance for improving the operating efficiency of the refrigeration cycle and guiding the actual liquid hydrogen production.
基金supported by the Ramanujan Fellowship from the Science and Engineering Research Board,Government of India(Grant No.RJF/2022/000115).
文摘This paper introduces dynamic mode decomposition(DMD)as a novel approach to model the breakage kinetics of particulate systems.DMD provides a data-driven framework to identify a best-fit linear dynamics model from a sequence of system measurement snapshots,bypassing the nontrivial task of determining appropriate mathemat-ical forms for the breakage kernel functions.A key innovation of our method is the instilling of physics-informed constraints into the DMD eigenmodes and eigenvalues,ensuring they adhere to the physical structure of particle breakage processes even under sparse measurement data.The integration of eigen-constraints is computationally aided by a zeroth-order global optimizer for solving the nonlinear,nonconvex optimization problem that elicits system dynamics from data.Our method is evaluated against the state-of-the-art optimized DMD algorithm using both generated data and real-world data of a batch grinding mill,showcasing over an order of magnitude lower prediction errors in data reconstruction and forecasting.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金supported by the National Natural Science Foundations of China(Grant Nos.12235007,12271324,and 11975131)。
文摘This paper explores the rich structure of peakon and pseudo-peakon solutions for a class of higher-order b-family equations,referred to as the J-th b-family(J-bF)equations.We propose several conjectures concerning the weak solutions of these equations,including a b-independent pseudo-peakon solution,a b-independent peakon solution,and a b-dependent peakon solution.These conjectures are analytically verified for J≤14 and/or J≤9 using the symbolic computation system MAPLE,which includes a built-in definition of the higher-order derivatives of the sign function.The b-independent pseudo-peakon solution is a 3rd-order pseudo-peakon for general arbitrary constants,with higher-order pseudo-peakons derived under specific parameter constraints.Additionally,we identify both b-independent and b-dependent peakon solutions,highlighting their distinct properties and the nuanced relationship between the parameters b and J.The existence of these solutions underscores the rich dynamical structure of the J-bF equations and generalizes previous results for lower-order equations.Future research directions include higher-order generalizations,rigorous proofs of the conjectures,interactions between different types of peakons and pseudo-peakons,stability analysis,and potential physical applications.These advancements significantly contribute to the understanding of peakon systems and their broader implications in mathematics and physics.
文摘Semisubmersible naval ships are versatile military crafts that combine the advantageous features of high-speed planing crafts and submarines.At-surface,these ships are designed to provide sufficient speed and maneuverability.Additionally,they can perform shallow dives,offering low visual and acoustic detectability.Therefore,the hydrodynamic design of a semisubmersible naval ship should address at-surface and submerged conditions.In this study,Numerical analyses were performed using a semisubmersible hull form to analyze its hydrodynamic features,including resistance,powering,and maneuvering.The simulations were conducted with Star CCM+version 2302,a commercial package program that solves URANS equations using the SST k-ωturbulence model.The flow analysis was divided into two parts:at-surface simulations and shallowly submerged simulations.At-surface simulations cover the resistance,powering,trim,and sinkage at transition and planing regimes,with corresponding Froude numbers ranging from 0.42 to 1.69.Shallowly submerged simulations were performed at seven different submergence depths,ranging from D/LOA=0.0635 to D/LOA=0.635,and at two different speeds with Froude numbers of 0.21 and 0.33.The behaviors of the hydrodynamic forces and pitching moment for different operation depths were comprehensively analyzed.The results of the numerical analyses provide valuable insights into the hydrodynamic performance of semisubmersible naval ships,highlighting the critical factors influencing their resistance,powering,and maneuvering capabilities in both at-surface and submerged conditions.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11562014,11762011,11671101,71471020,51839002the Natural Science Foundation of Inner Mongolia under Grant No.2017MS0108+4 种基金Hunan Provincial Natural Science Foundation of China under Grant No.2016JJ2061the Scientific Research Fund of Hunan Provincial Education Department under Grant No.18A325the Construct Program of the Key Discipline in Hunan Province under Grant No.201176the Aid Program for Science and Technology Innovative Research Team in Higher Educational Instituions of Hunan Province under Grant No.2014207Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering of Changsha University of Science and Technology under Grant No.018MMAEZD191
文摘In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.
文摘Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.
