二维平板间驻波声流的MRT-LBM数值研究

采用多松弛时间格子玻尔兹曼方法（Multiple Relaxation Time Lattice Boltzmann Method,MRT-LBM）对二维平板间的驻波声流进行数值模拟,模拟结果与Rayleigh流近似解析解相符,研究黏度和板间宽度对驻波声流的影响,得到不同黏度下x=L/4截面无量纲水平速度分布和x=L/2截面无量纲竖直速度分布,板间宽度对边界层内声流区域厚度的影响及驻波声流的形成过程,结果表明MRT-LBM模型能有效模拟驻波声流效应.     

Standing Waves in the Lorentz-Covariant World

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light.     

驻波法测超声波衰减系数

用驻波法测量超声波在空气中衰减系数的实验方法。与前人的方法进行比较。新的测量结果更符合实际。只有当换能器反射系数r〈0.619时,用简单波拟合得到的衰减系数才比较可信。同时讨论了该方法的实用意义。     

The Limits of Primary Radiation Forces in Bulk Acoustic Standing Waves for Concentrating Nanoparticles

Acoustic waves are increasingly used to concentrate, separate, and pattern nanoparticles in liquids, but the extent to which nanoparticles of different size and composition can be focused is not well‐defined. This article describes a simple analytical model for predicting the distribution of nanoparticles around the node of a 1D bulk acoustic standing wave over time as a function of pressure amplitude, acoustic contrast factor (i.e., nanoparticle and fluid composition), and size of the nanoparticles. Predictions from this model are systematically compared to results from experiments on gold nanoparticles of different sizes to determine the model's accuracy in estimating both the rate and the degree of nanoparticle focusing across a range of pressure amplitudes. The model is further used to predict the minimum particle size that can be focused for different nanoparticle and fluid compositions, and those predictions are tested with gold, silica, and polystyrene nanoparticles in water. A procedure combining UV‐light and photoacid is used to induce the aggregation of nanoparticles to illustrate the effect of nanoparticle aggregation on the observed degree of acoustic focusing. Overall, these findings clarify the extent to which acoustic resonating devices can be used to manipulate, pattern, and enrich nanoparticles suspended in liquids.     

利用气体火焰研究驻波

驻波是一个比较抽象的概念,较难理解,用气体火焰模拟驻波可以让我们更直观的研究声场产生的驻波。实验中发现火焰按波形变化的规律分布,用驻波波函数和伯努利方程对实验现象进行了理论分析,引入压节(波腹)、压腹(波节)解释在两端出现的高火焰现象。实验结果与理论分析接近一致。     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

On Ground-Traveling Waves for the Generalized Kadomtsev-Petviashvili Equations

As a continuation of our previous work, we improve some results on convergence of periodic KP traveling waves to solitary ones as the period goes to infinity. In addition, we present some qualitative properties of such waves, as well as nonexistence results, in the case of general nonlinearities. We suggest an approach which does not use any scaling argument. This revised version was published online in July 2006 with corrections to the Cover Date.     

Financial Rogue Waves

We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black Scholes model. These rogue wave solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.     

Financial Rogue Waves

We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These rogue wave solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.     

三维超声驻波场的数字全息测量与重建研究

利用数字全息干涉术研究了超声驻波场的三维分布特征,由所记录的不同角度的超声驻波场的数字全息图,经数值再现,得到了超声驻波场的强度和相位差分布图,进而由迭代重建算法重建出超声驻波场的三维分布曲线。结果表明,数字全息干涉术与迭代重建算法相结合是测量与重建三维超声驻波场的一种方便有效方法。     

Improved Speed and Shape of Ion-Acoustic Waves in a Warm Plasma

The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries (KdV) and nonlinear Schrödinger (NLS) equations. The rational solutions for the two equations has been obtained. The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations. The Sagdeev's potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation. The soliton and double layer solutions are obtained as a small amplitude approximation. A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed.     

Solving Nonlinear Wave Equations by Elliptic Equation

The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.     

Different-Periodic Travelling Wave Solutions for Nonlinear Equations

Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation, many new periodic travelling wave solutions with different periods and velocities are obtained based on the known periodic solutions. This procedure is crucially dependent on a sequence of cyclic identities involving Jacobi elliptic functions sn(ξ,m), cn(ξ,m), and dn(ξ,m).     

Approximate Solutions of Perturbed Nonlinear Schroedinger Equations

By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.     

A New Approach to Solve Nonlinear Wave Equations

From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.     

Extension of Variable Separable Solutions for Nonlinear Evolution Equations

We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.     

Applications of Computer Algebra in Solving Nonlinear Evolution Equations

With the use of computer algebra, the method that straightforwardly leads to travelling wave solutions is presented. The compound KdV--Burgers equation and KP--B equation are chosen to illustrate this approach. As a result, their abundant new soliton-like solutions and period form solutions are found.     

Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.