THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW

We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

ON NUMBER OF LIMIT CYCLES FOR THE QUADRATIC SYSTEMS WITH A WEAK FOCUS AND A STRONG FOCUS

It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.

A survey on delayed feedback control of chaos

This paper introduces the basic idea and provides the mathematical formulation of the delayed feedback control （DFC） methodology, which has been widely used in chaos control. Stability analysis including the well-known odd number linfitation of the DFC is reviewed. Some new developments in characterizing the limitation of the DFC are presented. Various modified DFC methods, which are developed in order to overcome the odd number limitation, are also described. Finally, some open problems in this research field are discussed.

INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAINS

The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

The Zero Mach Number Limit of the Three-Dimensional Compressible Viscous Magnetohydrodynamic Equations

This paper is concerned with the zero Mach number limit of the three-dimension- al compressible viscous magnetohydrodynamic equations. More precisely, based on the local existence of the three-dimensional compressible viscous magnetohydrodynamic equa- tions, first the convergence-stability principle is established. Then it is shown that, when the Much number is sufficiently small, the periodic initial value problems of the equations have a unique smooth solution in the time interval, where the incompressible viscous mag- netohydrodynamic equations have a smooth solution. When the latter has a global smooth solution, the maximal existence time for the former tends to infinity as the Much number goes to zero. Moreover, the authors prove the convergence of smooth solutions of the equa- tions towards those of the incompressible viscous magnetohydrodynamic equations with a sharp convergence rate.

CYCLE CONTR0L FUNCTIONS AND THE NUMBER 0F LIMIT CYCLES

The cycle coatrol function is defined and used to estimate tbe number of limit cycles for someplanar autonomous systems. Some sufficient conditions for the existence of no or at most one limitcycles are given.

Effects of resource additions on species richness and ANPP in an alpine meadow community

Aims Theories based on resource additions indicate that plant species richness is mainly determined by the number of limiting resources.However,the individual effects of various limiting resources on species richness and aboveground net primary productivity(ANPP)are less well understood.Here,we analyzed potential linkages between additions of limiting resources,species loss and ANPP increase and further explored the underlying mechanisms.Methods Resources(N,P,K and water)were added in a completely randomized block design to alpine meadow plots in the Qinghai-Tibetan Plateau.Plant aboveground biomass,species composition,mean plant height and light availability were measured in each plot.Regression and analysis of variance were used to analyze the responses of these measures to the different resource-addition treatments.Important Findings Species richness decreased with increasing number of added limiting resources,suggesting that plant diversity was apparently determined by the number of limiting resources.Nitrogen was the most important limiting resource affecting species richness,whereas Pand K alone had negligible effects.The largest reduction in species richness occurred when all three elements were added in combination.Water played a different role compared with the other limiting resources.Species richness increased when water was added to the treatments with N and P or with N,P and K.The decreases in species richness after resource additions were paralleled by increases in ANPP and decreases in light penetration into the plant canopy,suggesting that increased light competitionwas responsible for the negative effects of resource additions on plant species richness.

Thermal Behavior Analysis of Stacked-type Supercapacitors with Different Cell Structures

As a new energy storage element,supercapacitors have characteristics such as high power density,fast charge and discharge rates,green environmental protection,and long cycle life.Temperature is an important parameter of supercapacitors which significantly influences the stability of the supercapacitors.In this study,the finite element method is used to realize a coupling between a one-dimensional electrochemical model and a three-dimensional thermal model.Then,based on this model,the concept of limited cycle numbers is defined,and different unit quantities,unit size,and the effect of temperature under different temperature environments such as low temperature,room temperature,and high temperature on stacked-type supercapacitors is studied.Finally,stacked-type supercapacitors are compared with rolled-type supercapacitors considering the same cell size,density,and volume approximations.The simulation results show that the higher the number of packaging units,the lower is the limit cycle number.This phenomenon is more pronounced under high current than under low current conditions.Increasing the package size of the porous electrode or separator decreases the limiting cycles.Under the same unit volume scenario,improving the separator size proportion can accurately control the temperature rise at small current values.Under the same material,volume,and density approximations,the temperature rises slowly for stacked-type supercapacitors as compared to rolled-type supercapacitors.This phenomenon is more pronounced with an increase in current.

An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations

The computation of compressible flows becomesmore challengingwhen the Mach number has different orders of magnitude.When the Mach number is of order one,modern shock capturing methods are able to capture shocks and other complex structures with high numerical resolutions.However,if theMach number is small,the acoustic waves lead to stiffness in time and excessively large numerical viscosity,thus demanding much smaller time step and mesh size than normally needed for incompressible flow simulation.In this paper,we develop an all-speed asymptotic preserving(AP)numerical scheme for the compressible isentropic Euler and Navier-Stokes equations that is uniformly stable and accurate for all Mach numbers.Our idea is to split the system into two parts:one involves a slow,nonlinear and conservative hyperbolic system adequate for the use of modern shock capturing methods and the other a linear hyperbolic system which contains the stiff acoustic dynamics,to be solved implicitly.This implicit part is reformulated into a standard pressure Poisson projection system and thus possesses sufficient structure for efficient fast Fourier transform solution techniques.In the zero Mach number limit,the scheme automatically becomes a projection method-like incompressible solver.We present numerical results in one and two dimensions in both compressible and incompressible regimes.

The Perturbed Problem on the Boussinesq System of Rayleigh-Bénard Convection

In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞（0,t;H2（G）） is rigorously justified by analysis of asymptotic expansions.

The Incompressible Limits of Compressible Navier-Stokes Equations in the Whole Space with General Initial Data

It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz's estimate of linear wave equation.