The singular solutions to a nonsymmetric system of Keyfitz-Kranzer type with initial data of Riemann type

The solutions to the Riemann problem for a nonsymmetric system of Keyfitz-Kranzer type are constructed explicitly when the initial data are located in the quarter phase plane. In particular, some singular hyperbolic waves are discovered when one of the Riemann initial data is located on the boundary of the quarter phase plane, such as the delta shock wave and some composite waves in which the contact discontinuity coincides with the shock wave or the wave back of rarefaction wave. The double Riemann problem for this system with three piecewise constant states is also considered when the delta shock wave is involved. Furthermore, the global solutions to the double Riemann problem are constructed through studying the interaction between the delta shock wave and the other elementary waves by using the method of characteristics. Some interesting nonlinear phenomena are discovered during the process of constructing solutions; for example, a delta shock wave is decomposed into a delta contact discontinuity and a shock wave.     

Development of spiral wave in a regular network of excitatory neurons due to stochastic poisoning of ion channels

Some experimental evidences show that spiral wave could be observed in the cortex of brain, and the propagation of this spiral wave plays an important role in signal communication as a pacemaker. The profile of spiral wave generated in a numerical way is often perfect while the observed profile in experiments is not perfect and smooth. In this paper, formation and development of spiral wave in a regular network of Morris–Lecar neurons, which neurons are placed on nodes uniformly in a two-dimensional array and each node is coupled with nearest-neighbor type, are investigated by considering the effect of stochastic ion channels poisoning and channel noise. The formation and selection of spiral wave could be detected as follows. (1) External forcing currents with diversity are imposed on neurons in the network of excitatory neurons with nearest-neighbor connection, a target-like wave emerges and its potential mechanism is discussed; (2) artificial defects and local poisoned area are selected in the network to induce new wave to interact with the target wave; (3) spiral wave can be induced to occupy the network when the target wave is blocked by the artificial defects or poisoned area with regular border lines; (4) the stochastic poisoning effect is introduced by randomly modifying the border lines (areas) of specific regions in the network. It is found that spiral wave can be also developed to occupy the network under appropriate poisoning ratio. The process of growth for the poisoned area of ion channels poisoning is measured, the effect of channels noise is also investigated. It is confirmed that perfect spiral wave emerges in the network under gradient poisoning even if the channel noise is considered.     

Numerical Simulation of Detonation Excitation at Shock Wave Interaction with Dust Cloud in Channel

The study of detonation ability of reactive particle gas mixtures is necessary to prevent industrial explosions in industries where dispersed powders are used. The present paper focuses on numerical simulation of the shock wave interaction with semiinfinite aluminum dust cloud, which is situated inside a plane channel. The cloud fills entirely or partly the channel cross‐section and has initially a rectangular shape. The scenarios of detonation initiation in the cloud are determined depending on the incident shock wave amplitude values. The processes of transformation and spreading of finite width clouds under weak incident shock wave action (when the particles do not ignite) are investigated. The types of an oblique shock wave reflection from the plane of symmetry in the cloud are analyzed. The processes of particle ignition and detonation structure formation at strong incident shock wave action are investigated. Nonstationary periodic fuctuations take place in the detonation flow due to transversal wave effect. Nevertheless the detonation structure established propagates in quasistationary regime. If the incident shock wave is attenuated with a rarefaction wave then the detonation formation fails at clouds of insufficient width.     

强非线性广义 Boussinesq 方程孤波解的波形分析及求解

上海理工大学理学院\quad 上海 200093该文建立了强非线性广义 Boussinesq 方程的耗散项、波速、渐进值与波形函数的导数之间的关系.利用适当变换和待定假设方法,作者求出了上述广义 Boussinesq 方程的扭状或钟状孤波解,还求出了以前文献中未曾提到过的余弦函数的周期波解.进一步给出了波速对波形影响的结论,即:``好'广义 Boussinesq 方程的行波当波速由小变大时,波形由钟状孤波变成余弦函数周期波解;``坏'广义 Boussinesq 方程的行波当波速由小变大时,波形由余弦函数周期波解变成钟状孤波.     

Second order wave loads on large monolithic offshore structures

This paper considers the wave loads on large monolithic offshore structures. The second order wave force formulae developed by Rahman and Heaps, applicable to large circular cylinders in waves, are extended to evaluate the overturning moments on large circular cylinders. The theory is then applied to square section caissons in waves, to predict the wave loads on these structures. These calculations are performed using the exact form of the second order velocity potential, φ₂, with arbitrary wave number, k₂, and the approximate form of φ₂, with twice the value of the wave number of the first order velocity potential. The second order analytical predictions are compared with available experimental data for various ranges of wave parameters for both circular and square caissons in large amplitude waves.     

Steady solution of solitary wave and linear shear current interaction

The steady solution of a solitary wave propagating in the presence of a linear shear background current is investigated by the Green–Naghdi (GN) equations. The steady solution is obtained by use of the Newton–Raphson method. Three aspects are investigated; they are the wave speed, wave profile and velocity field. The converged GN results are compared with results from the literature. It is found that for the opposing-current case of the solitary wave with a small amplitude, the results of the GN equations match results from the literature well, while for the solitary wave with a large amplitude, results from the literature are seen to be not as accurate. In the following-current case, though the amplitude of the solitary wave is small, the GN results are shown to be accurate. The velocity along the water column at the wave crest and the velocity field for different cases are calculated by the GN equations. The results of the GN equations show obvious differences when compared with the results obtained by superposing the no-current results and linear shear current linearly. We find that for the same current strength, the vortex is stronger for the steep solitary-wave case than that for the small solitary-wave case.     

地形对正压大气Rossby波非线性相互作用的影响

本文采用弱非线性近似，推导出地形和Ｅｋｍａｎ摩擦共同作用下连续谱正压Ｒｏｓｓｂｙ波的非线性时空演化方程．根据这组方程，我们研究了窄角谱Ｒｏｓｓｂｙ波包的波波相互作用问题，当一个大振幅Ｒｏｓｓｂｙ波包通过大气传播时，如果它的振幅超过某个阈值，非线性相互作用会使一个尺度比它大的Ｒｏｓｓｂｙ波包和一个尺度比它小的Ｒｏｓｓｂｙ波包的振幅随时间指数增长，这两个次级波的本征频率会发生改变，Ｅｋｍａｎ摩擦、频率不匹配、地形坡度以及波包的空间演变共同决定了主波振幅的阈值及次级波本征频率的改变量．     

具有局部时间分数阶导数的非线性Zoomeron方程的精确解

In this paper, we are concerned with the nonlinear Zoomeron equation with local conformable time-fractional derivative. The concept of local conformable fractional derivative was newly proposed by R. Khalil et al. The bifurcation and phase portrait analysis of traveling wave solutions of the nonlinear Zoomeron equation are investigated. Moreover, by utilizing the exp(-?(ε))-expansion method and the first integral method, we obtained various exact analytical traveling wave solutions to the Zoomeron equation such as solitary wave, breaking wave and periodic wave.     

Boundedness and persistence of traveling wave solutions for a non-cooperative lattice-diffusion system with time delay

In this paper we study traveling wave solutions of a non-cooperative lattice-diffusion system with time delay, which includes predator–prey models and disease-transmission models. Minimal wave speed of traveling wave solutions is given. Schauder’s fixed-point theorem is applied to show the existence of semi-traveling wave solutions. The boundness and persistence of traveling wave solutions are overcome by using rescaling method and Laplace transform, where the application of Laplace transform to persistence is very novel and creative. The traveling wave solutions for some specific models are shown to connect to a positive equilibrium by using Lyapunov function and LaSalle’s invariance principle.     

Ocean-Atmosphere Interaction in the Lifecycle of ENSO： The Coupled Wave Oscillator

To explain the oscillatory nature of E1 Nino/Southern Oscillation （ENSO）, many ENSO theories emphasize the free oceanic equatorial waves propagating/reflecting within the Pacific Ocean, or the discharge/recharge of Pacific-basin-averaged ocean heat content. ENSO signals in the Indian and Atlantic oceans are often considered as remote response to the Pacific SST anomaly through atmospheric teleconnections. This study investigates the ENSO life cycle near the equator using long-term observational datasets. Space-time spectral analysis is used to identify and isolate the dominant interannual oceanic and atmospheric wave modes associated with ENSO. Nino3 SST anomaly is utilized as the ENSO index, and lag-correlation/regression are used to construct the composite ENSO life cycle. The propagation, structure and feedback mechanisms of the dominant wave modes are studied in detail. The results show that the dominant oceanic equatorial wave modes associated with ENSO are not free waves, but are two ocean-atmosphere coupled waves including a coupled Kelvin wave and waves are not confined only to the Pacific a coupled equatorial Rossby （ER） wave. These Ocean, but are of planetary scale with zonal wavenumbers 1-2, and propagate all the way around the equator in more than three years, leading to the longer than 3-year period of ENSO. When passing the continents, they become uncoupled atmospheric waves. The coupled Kelvin wave has larger variance than the coupled ER wave, making the total signals dominated by eastward propagation. Surface zonal wind stress （x） acts to slow down the waves. The two coupled waves interact with each other through boundary reflection and superposition, and they also interact with an off-equatorial Rossby wave in north Pacific along 15N through boundary reflection and wind stress forcing. The precipitation anomalies of the two coupled waves meet in the eastern Pacific shortly after the SST maximum of ENSO and excite a dry atmospheric Kelvin wave which quickly circles the whole equator and leads to a zonally symmetric signal of troposphere temperature. ENSO signals in the Indian and Atlantic oceans are associated with the two coupled waves as well as the fast atmospheric Kelvin wave. The discharge/recharge of Pacific-basin-averaged ocean heat content is also contributed by the two coupled waves. The above results suggest the presence of an alternative coupled wave oscillator mechanism for the oscillatory nature of ENSO.     

Degasperis-Procesi方程的孤立尖波解

利用动力系统的定性分析理论对D egasperis-P rocesi方程的孤立尖波解进行了研究.给出了D e-gasperis-P rocesi方程对应行波系统的相图分支,利用相图获得了孤立尖波解和周期尖波解的解析表达式,通过数值模拟给出了部分解的图像.     

Traveling wave fronts for generalized Fisher equations with spatio-temporal delays

We study the existence of traveling wave fronts for a reaction-diffusion equation with spatio-temporal delays and small parameters. The equation reduces to a generalized Fisher equation if small parameters are zero. We present two results. In the first one, we deal with the equation with very general kernels and show the persistence of Fisher wave fronts for all sufficiently small parameters. In the second one, we deal with some particular kernels, with which the nonlocal equation can be reduced to a system of singularly perturbed ODEs, and we are then able to apply the geometric singular perturbation theory and phase plane arguments to this system to show the existence of the minimal wave speed, the existence of a continuum of wave fronts, and the global uniqueness of the physical wave front with each wave speed.     

A finite-energywave process with given boundary conditions at one end and elastic clamping at the other end

The article considers uniqueness of the finite-energy generalized solution of the mixed boundary-initial value problem for a wave equation with elastic clamping. Excitation and relaxation problems for the wave process are solved analytically. The results are applied to solve the problem of boundary optimal control of the wave process.     

Stability of the planar rarefaction wave to two-dimensional Navier-Stokes-Korteweg equations of compressible fluids

This study is concerned with the large time behavior of the two-dimensional compressible Navier-Stokes-Korteweg equations, which are used to model compressible fluids with internal capillarity. Based on the fact that the rarefaction wave, one of the basic wave patterns to the hyperbolic conservation laws is nonlinearly stable to the one-dimensional compressible Navier-Stokes-Korteweg equations, the planar rarefaction wave to the two-dimensional compressible Navier-Stokes-Korteweg equations is first derived. Then, it is shown that the planar rarefaction wave is asymptotically stable in the case that the initial data are suitably small perturbations of the planar rarefaction wave. The proof is based on the delicate energy method. This is the first stability result of the planar rarefaction wave to the multi-dimensional viscous fluids with internal capillarity.     

Terminal Damping of a Solitary Wave Due to Radiation in Rotational Systems

The evolution of a solitary wave under the action of rotation is considered within the framework of the rotation-modified Korteweg–de Vries equation. Using an asymptotic procedure, the solitary wave is shown to be damped due to radiation of a dispersive wave train propagating with the same phase velocity as the solitary wave. Such a synchronism is possible because of the presence of rotational dispersion. The law of damping is found to be "terminal" in the sense that the solitary wave disappears in a finite time. The radiated wave amplitude and the structure of the radiated "tail" in space–time are also found. Some numerical results, which confirm the approximate theory developed here, are given.     

Peakon and cuspon solutions of a generalized Camassa-Holm-Novikov equation

The bounded traveling wave solutions of a generalized Camassa-Holm-Novikov equation with $p=2$ and $p=3$ are derived via the dynamical system approach. The singular wave solutions including peakons and cuspons are obtained by the bifurcation analysis of the corresponding singular dynamical system and the orbits intersecting with or approaching the singular lines. The results show that the generalized Camassa-Holm-Novikov equation with $p=2$ and $p=3$ both admit smooth solitary wave, smooth periodic wave solutions, solitary peakons, periodic peakons, solitary cuspons and periodic cuspons as well. It is worth pointing out that the Novikov equation has no bounded traveling wave solutions with negative wave speed, but has a family of new periodic cuspons which are distinguished with the normal periodic cuspons for their discontinuous first-order derivatives at both maximum and minimum.     

Recent progresses in studies on wave-current loads on foundation structure with piles and slab?

The foundation structure with piles and slab is widely used in o?shore wind farm construction in shallow water. Experimental studies on the hydrodynamic loads acting on the piles and slab under irregular waves and currents are summarized with discussion on the e?ects of pile grouping on the wave forces and wave impact loads on the slab locating near the free surface. By applying the theoretical solution of the wave di?racted by the slab and using the Morison equation to evaluate the wave force on the piles, the e?ects of the slab on the wave forces acting on the piles are analyzed. Based on the Reynolds-averaged Navier-Stokes (RANS) equations and the volume of ?uid (VOF) method, a numerical wave basin is developed to simulate the wave-structure interaction. The computed maximum wave force on the foundation structure with piles and slab agrees well with the measured data. The violent deformation, breaking, and run-up of the wave around the structure are presented and discussed. Further work on the turbulent ?ow structures and large deformation of the free surface due to interaction of the waves and foundation structures of o?shore wind farms needs more e?cient approaches for evaluating hydrodynamic loads under the e?ects of nonlinear waves and currents.     

Forced motion of breathers and domain boundaries against the background of nonlinear magnetization wave

Exact solutions of Landau–Lifshitz equation for a ferromagnet with an easy-axis anisotropy, which describe interaction of nonlinear precession wave of large amplitude with soliton-like objects, such as breathers, solitary domains and domain boundaries, are found by the “dressing” method. The change of the internal structure and physical parameters of solitons due to interaction with magnetization wave is analyzed. It is shown, that both solitary domains and domain walls move toward the wave. The conditions for the destruction of solitons by the nonlinear magnetization wave are obtained. An infinite series of integrals of motion, that stabilize the solitons on the background of magnetization wave, is found.     

外界场作用下的波前曲率关系和波形变化

研究外界场作用下,激发介质的波前曲率关系和波形变化·　理论分析波前曲率关系,得到外界场作用下,波前的法向速度与波前平均曲率、平面波速和外界场之间的线性关系·　数值分析外界场作用下,激发介质的Bar_Eiswirth模型,得到外界场作用下激发介质的波形图案·　这里的理论分析、数值结果与BZ反应的实验结果完全一致,从而解释了外界场作用下的BZ现象,且由数值结果可知激发介质包含丰富的波形图案·     

Permanent Wave Structures and Resonant Triads in a Layered Fluid

A closed three layer fluid with small density differences between the layers has two closely related modes of gravity wave propagation. The nonlinear interactions between the wave modes are investigated, particularly the nearly resonant or significant interactions. Permanent wave solutions are calculated, and it is shown that a permanent wave of the slower mode can generate resonantly a wave harmonic of the faster mode. The equations governing resonant triads of the two modes are derived, and solutions having a permanent structure are calculated from them. It is found that some resonant triad solutions vanish when the triad is embedded in the set of all harmonics with wavenumbers in its neighborhood