This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of...This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.展开更多
In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)~1-u.The continuity of c(m, f) in m and ...In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)~1-u.The continuity of c(m, f) in m and f is also proved. Especially, for f(u)=1-u, the estimateof the minimal wave speed c(m, f) is obtained.展开更多
Seismic wave interaction with a slippery rock joint with an arbitrary impinging angle is analytically studied based on the conservation of momentum on the wave fronts. Based on the displacement discontinuity method, t...Seismic wave interaction with a slippery rock joint with an arbitrary impinging angle is analytically studied based on the conservation of momentum on the wave fronts. Based on the displacement discontinuity method, the wave propagation equations are derived for incident P- and S-waves. By comparison, the calculated transmission and reflection coefficients for normal incident waves are the same as the existing results, which proves the wave propagation equation obtained in the paper is correct. The wave propagation derived in the context can be applied to incident waves with different waveforms. Stochastic seismic waves are then used to analyze the seismic wave interaction with the slippery rock joint, where the stochastic seismic waves are generated from frequency spectra. The parametric studies are carried out to investigate the effect of type, intensity and impinging angle of the incident seismic waves on the wave propagation across the slippery rock joint.展开更多
RDX and TNT based explosives are very useful in performing research and development works especially when complex shaping of an assembly is required due to their molding capability and the range of ratios in which the...RDX and TNT based explosives are very useful in performing research and development works especially when complex shaping of an assembly is required due to their molding capability and the range of ratios in which they can be mixed. In this paper, for these compositions, detonation shock dynamics (DSD) relations between normal detonation velocity D. and detonation wave curvature κ are determined for RDX: TNT explosives in weight ratios 40:60, 50:50 and 60:40. Experiments are performed with 50 mm diameter rate sticks of approximately 200 mm length using high speed rotating mirror camera and time measurement probes. The results show that first order DSD relation is indeed representative of these explosives. The slope of this relation increases by increasing TNT contents in these explosives. Going from 40% to 60% TNT, the data show an increase of more than 100% in negative slope of Dn-κ relation.展开更多
This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a...This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a subset can be constructed. We then apply the Schauder's fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.展开更多
This paper deals with the study of transient waves in a homogeneous isotropic,solid halfspace with a permeating substance in the context of the theory of generalized elasto-thermodiffusion.The halfspace is assumed to ...This paper deals with the study of transient waves in a homogeneous isotropic,solid halfspace with a permeating substance in the context of the theory of generalized elasto-thermodiffusion.The halfspace is assumed to be disturbed due to mechanical loads acting on its boundary.The model comprising of basic governing differential equations and boundary conditions has been solved by employing Laplace transform technique.Noting that the second sound effects are short lived,the small time approximations of solution for various physical quantities have been obtained and the results are discussed on the possible wave fronts.In case of continuous and periodic loads acting at the boundary,the displacement is found to be continuous at each wave front while it is discontinuous in case of impulsive load.The temperature and concentration fields are found to be discontinuous at all the wave fronts.The displacement,temperature change and concentration deviation due to impulsive,continuous and periodic mechanical loads have also been evaluated in the physical domain at all times by employing numerical inversion technique of integral transform.The computer simulated numerical results have been presented graphically in respect of displacement,temperature change and concentration deviation for brass.A significant effect of mass diffusion has been observed on the behaviour of mechanical and thermal waves.展开更多
This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spa...This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spatial domain R.When the delay kernel is assumed to be the strong generic kernel,using the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.展开更多
基金supported by the China Postdoctoral Science Foundation(No.2020M670963)supported by the Natural Science Foundation of China(No.12071297)the Natural Science Foundation of Shanghai(No.18ZR1426500).
文摘This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.
基金This project is supported by the Doctoral Programme Foundation of Institution of Higher Education
文摘In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)~1-u.The continuity of c(m, f) in m and f is also proved. Especially, for f(u)=1-u, the estimateof the minimal wave speed c(m, f) is obtained.
基金Supported by the National Natural Science Foundation of China (11072257, 51025935, 40872188)the Key Projects in the National Sciences and Technology Pillar Program (2008DAB29B00)
文摘Seismic wave interaction with a slippery rock joint with an arbitrary impinging angle is analytically studied based on the conservation of momentum on the wave fronts. Based on the displacement discontinuity method, the wave propagation equations are derived for incident P- and S-waves. By comparison, the calculated transmission and reflection coefficients for normal incident waves are the same as the existing results, which proves the wave propagation equation obtained in the paper is correct. The wave propagation derived in the context can be applied to incident waves with different waveforms. Stochastic seismic waves are then used to analyze the seismic wave interaction with the slippery rock joint, where the stochastic seismic waves are generated from frequency spectra. The parametric studies are carried out to investigate the effect of type, intensity and impinging angle of the incident seismic waves on the wave propagation across the slippery rock joint.
文摘RDX and TNT based explosives are very useful in performing research and development works especially when complex shaping of an assembly is required due to their molding capability and the range of ratios in which they can be mixed. In this paper, for these compositions, detonation shock dynamics (DSD) relations between normal detonation velocity D. and detonation wave curvature κ are determined for RDX: TNT explosives in weight ratios 40:60, 50:50 and 60:40. Experiments are performed with 50 mm diameter rate sticks of approximately 200 mm length using high speed rotating mirror camera and time measurement probes. The results show that first order DSD relation is indeed representative of these explosives. The slope of this relation increases by increasing TNT contents in these explosives. Going from 40% to 60% TNT, the data show an increase of more than 100% in negative slope of Dn-κ relation.
基金Supported by the National Natural Science Foundation of China(No.19971032)the second author is supported by Natural Science Foundation of Canadaby a Petro Canada Young Innovator Award.
文摘This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a subset can be constructed. We then apply the Schauder's fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.
文摘This paper deals with the study of transient waves in a homogeneous isotropic,solid halfspace with a permeating substance in the context of the theory of generalized elasto-thermodiffusion.The halfspace is assumed to be disturbed due to mechanical loads acting on its boundary.The model comprising of basic governing differential equations and boundary conditions has been solved by employing Laplace transform technique.Noting that the second sound effects are short lived,the small time approximations of solution for various physical quantities have been obtained and the results are discussed on the possible wave fronts.In case of continuous and periodic loads acting at the boundary,the displacement is found to be continuous at each wave front while it is discontinuous in case of impulsive load.The temperature and concentration fields are found to be discontinuous at all the wave fronts.The displacement,temperature change and concentration deviation due to impulsive,continuous and periodic mechanical loads have also been evaluated in the physical domain at all times by employing numerical inversion technique of integral transform.The computer simulated numerical results have been presented graphically in respect of displacement,temperature change and concentration deviation for brass.A significant effect of mass diffusion has been observed on the behaviour of mechanical and thermal waves.
基金Supported by the National Natural Science Foundation of China (10961017)
文摘This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spatial domain R.When the delay kernel is assumed to be the strong generic kernel,using the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.