Quasi-periodic and Non-periodic Waves in （2q-1）-Dimensional Nonlinear Systems

New exact quasi-periodic and non-periodic solutions for the （2＋ 1）-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach （MLVSA） and the Jacobi elliptic functions with the space-time-dependent modulus. Though the result is valid for all the MLVSA solvable models, it is explicitly shown for the long-wave and short-wave interaction model.

Multi-focus non-periodic scanning method for femtosecond lasers based on DMD and galvanometer scanners[Invited]

Multi-focus parallel scanning can effectively increase laser fabrication throughput.However,the conventional approach of using a spatial light modulator(SLM)to generate multi-foci and scan this fixed number of foci with galvanometer scanners can only achieve a periodic scanning trajectory due to the low switching speed of the SLM.Here we demonstrate a multifocus non-periodic scanning method for femtosecond lasers by using,instead,a fast-switching digital micromirror device(DMD)to generate a dynamic number of foci.The number of effective foci is quickly switched by introducing aberration to the undesired focus.In this way,the intensity allocated to each focus will not be affected by the number of foci,and a uniformity of 98%with different numbers of foci is achieved without adjusting the total laser energy.Finally,we validate the effectiveness of this scanning method by demonstrating corneal flap fabrication of porcine cornea in vitro.

Study on the instantaneous protection reliability of low voltage circuit breakers

This paper outlines the significance of enhancing the instantaneous protection reliability of low voltage circuit breakers and describes their main failure modes. The instantaneous failure mechanism of low voltage circuit breakers was analyzed so that measures to improve instantaneous protection reliability can be determined. Furthermore, the theory of the instantaneous characteristics calibration device for low voltage circuit breakers and the method of eliminating the non-periodic component of test current are given in detail. Finally, the test results are presented.

The Tessellation Rule and Properties Programming of Origami Metasheets Built with a Mixture of Rigid and Non-Rigid Square-Twist Patterns

Metamaterials constructed from origami units of different types and behaviors could potentially offer a broader scope of mechanical properties than those formed from identical unit types.However,the geometric design rules and property programming methods for such metamaterials have yet to be extensively explored.In this paper,we propose a new kind of origami metasheet by incorporating a family of different square-twist units.The tessellation rule of these metasheets is established to allow compatible mountain-valley crease assignments and geometric parameters among neighboring units.We demonstrate through experiments that the energy,initial peak force,and maximum stiffness of the metasheets can be obtained by a summation of the properties of the constitutional units.Based on this,we are able to program the mechanical properties of the metasheets over a wide range by varying the types and proportions of the units,as well as their geometric and material parameters.Furthermore,for a metasheet with a fixed number of units,all the geometrically compatible tessellations can be folded out of the same pre-creased sheet material by simply changing the mountain-valley assignments,thereby allowing the properties of the metasheet to be re-programmed based on specific requirements.This work could inspire a new class of programmable origami metamaterials for current and future mechanical and other engineering applications.

Characteristics Collocation Method of Compressible Miscible Displacement with Dispersion

The compressible miscible displacement in a porous media is considered in this paper. The problem is a nonlinear system with dispersion in non-periodic space. The concentration is treated by a characteristics collocation method, and the pressure is treated by an orthogonal collocation method. Optimal order estimates are derived.

On the universal third order Stokes wave solution

This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.

Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

ASYMPTOTIC BEHAVIOR OF QUASI－COMPETITIVE SPECIES DEFINED BYLOTKA－VOLTERRA DYNAMICS

Competitive systems defined by Lotka-Volterra equations where ri>0, aij>0, have been extensively studied in the literature. Much attention has been drawn to, among other things, the non-periodic oscillation phenomenon, or May-type trajectory as it is called by some authors, since the discovery of that kind of trajectories in competitive LotkaVolterra systems made by May and Leonard[2] . Recently, the same phenomenon was reported to be existing in prey-predator systems. In this paper it is clear that one can expect the appearance of such phenomenon in a broader class of Lotka-Volterra systems, namely quasi-competitive systems (i.e. ri >0, (aij/ajj)+(aji/aii)>0 in (I)), which cover both competitive and some prey-predator systems in addition to others. Conditions are established in terms of the parameters of the systems for the existence of stable equilibrium, periodic oscillation and non-periodic oscillation.

The Theory of Composite Characteristics Under Sampling Scheme Without Discontinuing Inspection

In this paper,we establish the model of a finite,irreducible non-periodic and ergodic Markov chain for the sampling scheme without discotinuing state,then calculate and analyse the composite characteristics of a three-level skip-lot sampling scheme.