A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance con...A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.展开更多
The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to ...The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.展开更多
In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the...In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the tethered combination system in the post-capture phase was established with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether.The motion law of the tethered combination in the deorbiting process with different disturbances was simulated and discussed on the premise that the platform was only controlled by a constant thrust force.It is known that the four motion freedoms of the tethered combination are coupled with each other in the deorbiting process from the simulation results.A noticeable phenomenon is that the tether longitudinal vibration does not decay to vanish even under the large tether damping with initial attitude disturbances due to the coupling effect.The approximate analytical solutions of the dynamics for a simplified model are obtained through the perturbation method.The condition of the inter resonance phenomenon is the frequency ratio λ_1=2.The case study shows good accordance between the analytical solutions and numerical results,indicating the effectiveness and correctness of approximate analytical solutions.展开更多
With the L-P approximate method(variation of parameter method), a barotropic channel model in β-plane is used to study the effect of nonlinear interaction between two waves with different scales on the formation of b...With the L-P approximate method(variation of parameter method), a barotropic channel model in β-plane is used to study the effect of nonlinear interaction between two waves with different scales on the formation of blocking. The approximate analytical solution, which can describe the process of the blocking formation, maintenance and breakdown, has been obtained by using the method of aproximate expansion. The importance of nonlinear interaction between two waves with different scales is stressed in the solution. The result suggests that the nonlinear interaction is the main dynamic process of the blocking formation. Some required conditions of blocking formation are also discussed.展开更多
A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of ...A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.展开更多
On 12 December 2019,a novel coronavirus disease,named COVID-19,began to spread around the world from Wuhan,China.It is useful and urgent to consider the future trend of this outbreak.We establish the 4+1 penta-group m...On 12 December 2019,a novel coronavirus disease,named COVID-19,began to spread around the world from Wuhan,China.It is useful and urgent to consider the future trend of this outbreak.We establish the 4+1 penta-group model to predict the development of the COVID-19 outbreak.In this model,we use the collected data to calibrate the parameters,and let the recovery rate and mortality change according to the actual situation.Furthermore,we propose the BAT model,which is composed of three parts:simulation of the return rush(Back),analytic hierarchy process(AHP)method,and technique for order preference by similarity to an ideal solution(TOPSIS)method,to figure out the best return date for university students.We also discuss the impacts of some factors that may occur in the future,such as secondary infection,emergence of effective drugs,and population flow from Korea to China.展开更多
In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random p...In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process.The proposed method has the advantage of obtaining the response＇s moments directly from the initial conditions and statistical characteristics of the corresponding external excitations. First, the response＇s moment equations are directly derived based on a DPA, which is completely independent of the It？/filtering approach since no specific assumptions regarding the correlation structure of excitation are made.By solving them under Gaussian closure, the response＇s moments can be obtained. Subsequently, a multiscale algorithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo（MC） simulation gives good agreement.Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.展开更多
An exhaustive study of the noncontinuous-state laser dynamics associated with the transient optical process is significant because it reveals the complex physical mechanisms and characteristics in nonlinear laser syst...An exhaustive study of the noncontinuous-state laser dynamics associated with the transient optical process is significant because it reveals the complex physical mechanisms and characteristics in nonlinear laser systems.In this study,in-depth theoretical interpretation and experimental verification of the noncontinuous-state dynamics in laser system are presented,based on developed pulse-modulated frequency-shifted laser feedback interferometry(LFI).By introducing external pulse modulation,we investigate the nonlinear time-of-flight dynamics and related photon behaviors evolution of the pulsed LFI system by observing the changes in effective interference time sequences for interference realization and attainable minimum feedback photon number of the signal under various modulated noncontinuous states.Implementation of the pulse-modulated LFI scheme should exceed the pulse overlapping time window limit of 1.93μs to effectively extract and preserve the extracavity feedback photon information.Experiments reveal that the minimum feedback photon number of signals successfully measured by the pulsed LFI sensor is 0.067 feedback photons per Doppler cycle,exhibiting high sensitivity for extremely weak signal detection.Further,simultaneous measurement for velocity and distance of the moving object is performed to validate the feasibility and applicability of the pulsed LFI.The system can successfully achieve large-range simultaneous measurements within the velocity range of 73.5-612.6 mm∕s,over a distance of 25.5 km.This work opens the way to unexplored frontiers of pulsed LFI to fill the research gap in noncontinuous laser dynamics in this field,showcasing diverse and wide-ranging applications in the realm of integrated sensing,remote monitoring,and positioning and navigation.展开更多
Over 1.3 million people die annually in traffic accidents,and this tragic fact highlights the urgent need to enhance the intelligence of traffic safety and control systems.In modern industrial and technological applic...Over 1.3 million people die annually in traffic accidents,and this tragic fact highlights the urgent need to enhance the intelligence of traffic safety and control systems.In modern industrial and technological applications and collaborative edge intelligence,control systems are crucial for ensuring efficiency and safety.However,deficiencies in these systems can lead to significant operational risks.This paper uses edge intelligence to address the challenges of achieving target speeds and improving efficiency in vehicle control,particularly the limitations of traditional Proportional-Integral-Derivative(PID)controllers inmanaging nonlinear and time-varying dynamics,such as varying road conditions and vehicle behavior,which often result in substantial discrepancies between desired and actual speeds,as well as inefficiencies due to manual parameter adjustments.The paper uses edge intelligence to propose a novel PID control algorithm that integrates Backpropagation(BP)neural networks to enhance robustness and adaptability.The BP neural network is first trained to capture the nonlinear dynamic characteristics of the vehicle.Thetrained network is then combined with the PID controller to forma hybrid control strategy.The output layer of the neural network directly adjusts the PIDparameters(k_(p),k_(i),k_(d)),optimizing performance for specific driving scenarios through self-learning and weight adjustments.Simulation experiments demonstrate that our BP neural network-based PID design significantly outperforms traditional methods,with the response time for acceleration from 0 to 1 m/s improved from 0.25 s to just 0.065 s.Furthermore,real-world tests on an intelligent vehicle show its ability to make timely adjustments in response to complex road conditions,ensuring consistent speed maintenance and enhancing overall system performance.展开更多
The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most ...The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most one particle can occupy each site.We mostly discuss the symmetric and reversible case.The weakly asymmetric case recently attracts attention related to KPZ equation;cf.Bertini and Giacomin(Commun Math Phys 183:571–607,1995)for a simple exclusion case and Gonçalves and Jara(Arch Ration Mech Anal 212:597–644,2014)for an exclusion process with speed change,see also Gonçalves et al.(Ann Probab 43:286–338,2015),Gubinelli and Perkowski(J Am Math Soc 31:427–471,2018).In Sect.1,as a warm-up,we consider a simple exclusion process and discuss its hydrodynamic limit and the corresponding fluctuation limit in a proper space–time scaling.From this model,one can derive a linear heat equation and a stochastic partial differential equation(SPDE)in the limit,respectively.Section 2 is devoted to the entropy method originally invented by Guo et al.(Commun Math Phys 118:31–59,1988).We consider the exclusion process with speed change,in which the jump rate of a particle depends on the configuration nearby the particle.This gives a non-trivial interaction among particles.We study only the case that the jump rate satisfies the so-called gradient condition.The hydrodynamic limit,which leads to a nonlinear diffusion equation,follows from the local ergodicity or the local equilibrium of the system,and this is shown by establishing one-block and twoblock estimates.We also discuss the fluctuation limit which follows by showing the so-called Boltzmann–Gibbs principle.Section 3 explains the relative entropy method originally due to Yau(Lett Math Phys 22:63–80,1991).This is a variant of GPV method and gives another proof for the hydrodynamic limit.The difference between these two methods is as follows.Let N^(d)be the volume of the domain on which the system is defined(typically,d-dimensional discrete box with side length N)and denote the(relative)entropy by H.Then,H relative to a global equilibrium behaves as H=O(N^(d))(or entropy per volume is O(1))as N→∞.GPV method rather relies on the fact that the entropy production I,which is the time derivative of H,behaves as O(N^(d−2))so that I per volume is o(1),and this characterizes the limit measures.On the other hand,Yau’s method shows H=o(Nd)for H relative to local equilibria so that the entropy per volume is o(1)and this proves the hydrodynamic limit.In Sect.4,we considerKawasaki dynamics perturbed by relatively largeGlauber effect,which allows creation and annihilation of particles.This leads to the reaction–diffusion equation in the hydrodynamic limit.We discuss especially the equation with reaction term of bistable type and the problem related to the fast reaction limit or the sharp interface limit leading to the motion by mean curvature.We apply the estimate on the relative entropy due to Jara and Menezes(Non-equilibrium fluctuations of interacting particle systems,2017;Symmetric exclusion as a random environment:invariance principle,2018),which is actually obtained as a combination of GPV and Yau’s estimates.This makes possible to study the hydrodynamic limit for microscopic systems with another diverging factors apart from that caused by the space–time scaling.展开更多
文摘A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.
基金supported by the major advanced research project of Civil Aerospace from State Administration of Science,Technology and Industry of China.
文摘The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.
基金Project (51475411) supported by the National Natural Science Foundation of ChinaProject (LY15E070002) supported by Zhejiang Provincial Natural Science Foundation of China
文摘In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the tethered combination system in the post-capture phase was established with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether.The motion law of the tethered combination in the deorbiting process with different disturbances was simulated and discussed on the premise that the platform was only controlled by a constant thrust force.It is known that the four motion freedoms of the tethered combination are coupled with each other in the deorbiting process from the simulation results.A noticeable phenomenon is that the tether longitudinal vibration does not decay to vanish even under the large tether damping with initial attitude disturbances due to the coupling effect.The approximate analytical solutions of the dynamics for a simplified model are obtained through the perturbation method.The condition of the inter resonance phenomenon is the frequency ratio λ_1=2.The case study shows good accordance between the analytical solutions and numerical results,indicating the effectiveness and correctness of approximate analytical solutions.
文摘With the L-P approximate method(variation of parameter method), a barotropic channel model in β-plane is used to study the effect of nonlinear interaction between two waves with different scales on the formation of blocking. The approximate analytical solution, which can describe the process of the blocking formation, maintenance and breakdown, has been obtained by using the method of aproximate expansion. The importance of nonlinear interaction between two waves with different scales is stressed in the solution. The result suggests that the nonlinear interaction is the main dynamic process of the blocking formation. Some required conditions of blocking formation are also discussed.
基金National Natural Science Foundation of China (60572023)
文摘A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.
基金the National Key Research and Development Program of China(No.2018YFB1004700)the National Natural Science Foundation of China(Nos.61872238 and 61972254)+1 种基金the Shanghai Science and Technology Fund(No.17510740200)the CCF-Huawei Database System Innovation Research Plan(No.CCF-Huawei DBIR2019002A)。
文摘On 12 December 2019,a novel coronavirus disease,named COVID-19,began to spread around the world from Wuhan,China.It is useful and urgent to consider the future trend of this outbreak.We establish the 4+1 penta-group model to predict the development of the COVID-19 outbreak.In this model,we use the collected data to calibrate the parameters,and let the recovery rate and mortality change according to the actual situation.Furthermore,we propose the BAT model,which is composed of three parts:simulation of the return rush(Back),analytic hierarchy process(AHP)method,and technique for order preference by similarity to an ideal solution(TOPSIS)method,to figure out the best return date for university students.We also discuss the impacts of some factors that may occur in the future,such as secondary infection,emergence of effective drugs,and population flow from Korea to China.
基金supported by the Defense Industrial Technology Development Program (Grant JCKY2013601B)the "111" Project (Grant B07009)the National Natural Science Foundation of China (Grants 11372025, 11432002)
文摘In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process.The proposed method has the advantage of obtaining the response＇s moments directly from the initial conditions and statistical characteristics of the corresponding external excitations. First, the response＇s moment equations are directly derived based on a DPA, which is completely independent of the It？/filtering approach since no specific assumptions regarding the correlation structure of excitation are made.By solving them under Gaussian closure, the response＇s moments can be obtained. Subsequently, a multiscale algorithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo（MC） simulation gives good agreement.Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.
基金National Natural Science Foundation of China(62275001,62105001)China Postdoctoral Science Foundation(GZC20242187)Zhejiang Province Postdoctoral Research Funding(ZJ2024097)。
文摘An exhaustive study of the noncontinuous-state laser dynamics associated with the transient optical process is significant because it reveals the complex physical mechanisms and characteristics in nonlinear laser systems.In this study,in-depth theoretical interpretation and experimental verification of the noncontinuous-state dynamics in laser system are presented,based on developed pulse-modulated frequency-shifted laser feedback interferometry(LFI).By introducing external pulse modulation,we investigate the nonlinear time-of-flight dynamics and related photon behaviors evolution of the pulsed LFI system by observing the changes in effective interference time sequences for interference realization and attainable minimum feedback photon number of the signal under various modulated noncontinuous states.Implementation of the pulse-modulated LFI scheme should exceed the pulse overlapping time window limit of 1.93μs to effectively extract and preserve the extracavity feedback photon information.Experiments reveal that the minimum feedback photon number of signals successfully measured by the pulsed LFI sensor is 0.067 feedback photons per Doppler cycle,exhibiting high sensitivity for extremely weak signal detection.Further,simultaneous measurement for velocity and distance of the moving object is performed to validate the feasibility and applicability of the pulsed LFI.The system can successfully achieve large-range simultaneous measurements within the velocity range of 73.5-612.6 mm∕s,over a distance of 25.5 km.This work opens the way to unexplored frontiers of pulsed LFI to fill the research gap in noncontinuous laser dynamics in this field,showcasing diverse and wide-ranging applications in the realm of integrated sensing,remote monitoring,and positioning and navigation.
基金supported by the National Key Research and Development Program of China(No.2023YFF0715103)-financial supportNational Natural Science Foundation of China(Grant Nos.62306237 and 62006191)-financial support+1 种基金Key Research and Development Program of Shaanxi(Nos.2024GX-YBXM-149 and 2021ZDLGY15-04)-financial support,NorthwestUniversity Graduate Innovation Project(No.CX2023194)-financial supportNatural Science Foundation of Shaanxi(No.2023-JC-QN-0750)-financial support.
文摘Over 1.3 million people die annually in traffic accidents,and this tragic fact highlights the urgent need to enhance the intelligence of traffic safety and control systems.In modern industrial and technological applications and collaborative edge intelligence,control systems are crucial for ensuring efficiency and safety.However,deficiencies in these systems can lead to significant operational risks.This paper uses edge intelligence to address the challenges of achieving target speeds and improving efficiency in vehicle control,particularly the limitations of traditional Proportional-Integral-Derivative(PID)controllers inmanaging nonlinear and time-varying dynamics,such as varying road conditions and vehicle behavior,which often result in substantial discrepancies between desired and actual speeds,as well as inefficiencies due to manual parameter adjustments.The paper uses edge intelligence to propose a novel PID control algorithm that integrates Backpropagation(BP)neural networks to enhance robustness and adaptability.The BP neural network is first trained to capture the nonlinear dynamic characteristics of the vehicle.Thetrained network is then combined with the PID controller to forma hybrid control strategy.The output layer of the neural network directly adjusts the PIDparameters(k_(p),k_(i),k_(d)),optimizing performance for specific driving scenarios through self-learning and weight adjustments.Simulation experiments demonstrate that our BP neural network-based PID design significantly outperforms traditional methods,with the response time for acceleration from 0 to 1 m/s improved from 0.25 s to just 0.065 s.Furthermore,real-world tests on an intelligent vehicle show its ability to make timely adjustments in response to complex road conditions,ensuring consistent speed maintenance and enhancing overall system performance.
文摘The exclusion process,sometimes called Kawasaki dynamics or lattice gas model,describes a system of particles moving on a discrete square lattice with an interaction governed by the exclusion rule under which at most one particle can occupy each site.We mostly discuss the symmetric and reversible case.The weakly asymmetric case recently attracts attention related to KPZ equation;cf.Bertini and Giacomin(Commun Math Phys 183:571–607,1995)for a simple exclusion case and Gonçalves and Jara(Arch Ration Mech Anal 212:597–644,2014)for an exclusion process with speed change,see also Gonçalves et al.(Ann Probab 43:286–338,2015),Gubinelli and Perkowski(J Am Math Soc 31:427–471,2018).In Sect.1,as a warm-up,we consider a simple exclusion process and discuss its hydrodynamic limit and the corresponding fluctuation limit in a proper space–time scaling.From this model,one can derive a linear heat equation and a stochastic partial differential equation(SPDE)in the limit,respectively.Section 2 is devoted to the entropy method originally invented by Guo et al.(Commun Math Phys 118:31–59,1988).We consider the exclusion process with speed change,in which the jump rate of a particle depends on the configuration nearby the particle.This gives a non-trivial interaction among particles.We study only the case that the jump rate satisfies the so-called gradient condition.The hydrodynamic limit,which leads to a nonlinear diffusion equation,follows from the local ergodicity or the local equilibrium of the system,and this is shown by establishing one-block and twoblock estimates.We also discuss the fluctuation limit which follows by showing the so-called Boltzmann–Gibbs principle.Section 3 explains the relative entropy method originally due to Yau(Lett Math Phys 22:63–80,1991).This is a variant of GPV method and gives another proof for the hydrodynamic limit.The difference between these two methods is as follows.Let N^(d)be the volume of the domain on which the system is defined(typically,d-dimensional discrete box with side length N)and denote the(relative)entropy by H.Then,H relative to a global equilibrium behaves as H=O(N^(d))(or entropy per volume is O(1))as N→∞.GPV method rather relies on the fact that the entropy production I,which is the time derivative of H,behaves as O(N^(d−2))so that I per volume is o(1),and this characterizes the limit measures.On the other hand,Yau’s method shows H=o(Nd)for H relative to local equilibria so that the entropy per volume is o(1)and this proves the hydrodynamic limit.In Sect.4,we considerKawasaki dynamics perturbed by relatively largeGlauber effect,which allows creation and annihilation of particles.This leads to the reaction–diffusion equation in the hydrodynamic limit.We discuss especially the equation with reaction term of bistable type and the problem related to the fast reaction limit or the sharp interface limit leading to the motion by mean curvature.We apply the estimate on the relative entropy due to Jara and Menezes(Non-equilibrium fluctuations of interacting particle systems,2017;Symmetric exclusion as a random environment:invariance principle,2018),which is actually obtained as a combination of GPV and Yau’s estimates.This makes possible to study the hydrodynamic limit for microscopic systems with another diverging factors apart from that caused by the space–time scaling.
