非线性势场与多扭结子解之间的关系

通过对非线性场方程扭结子（ｋｉｎｋ）解的研究，发现了静态场方程解φｎ 都可由φ２ 迭加组合构成．并由此得出场变量φｎ 相应的势场函数．

非线性基底势对离散非线性晶格孤波动力学性质的影响

使用一种简化的准离散多重尺度法,研究了具有非线性基底势的一维离散非线性晶格的孤波解,表明孤波能够在这种一维非线性晶格链中存在,而且非线性基底势对孤波的载波频率、群速度、振幅等动力学性质都将产生影响.另一方面,我们还对非线性动力学方程进行了数值求解,发现用简化的准离散多重尺度法得到的近似解与精确的计算机数值计算结果符合得较好.

非线性δ势的透射特征

研究了非线性δ势的透射特征,并与线性情况做了对比.

等离子体中非线性二维德拜屏蔽的精确解析解

研究了等离子体中非线性二维德拜屏蔽 ,首次给出了二维泊松方程的一些新的精确解析解 .对于一些特殊情况 。

与有限热浴耦合的布朗粒子的演化行为研究

本文重点考查与有限热浴耦合的布朗粒子的非各态历经和非平衡性.在广义朗之万方程框架下,基于拉普拉斯变换理论推导得出粒子演化的精确解,并进一步探究粒子的渐进行为.研究发现即使在非线性势束缚作用下,粒子的稳态行为依赖于初始坐标,而与初始速度无关,呈现非各态历经性.数值模拟结果表明,只初始坐标分布取Gibbs-Boltzmann分布时,粒子才有可能达到平衡态.

附加阻尼影响下的极地破冰船波浪增阻研究

考虑到极地破冰船典型的破冰型船艏会对大洋航行阻力性能产生不利的影响,进而对其波浪增阻性能展开研究。基于三维非线性势流理论,以线性加平方的阻尼模型等效考虑船体黏性横摇阻尼,研究了极地破冰船在不同浪向下波浪增阻特性。进一步地,考虑减摇装置带来的等效附加阻尼,研究附加阻尼对艏斜浪下波浪增阻的影响规律,分析附加阻尼对波浪中阻力时历曲线的各阶幅值的影响。研究发现,附加阻尼对部分海况条件下波浪增阻有减弱作用,降低了船体阻力时历曲线的非线性,对极地破冰船大洋航行起到改善作用。

ALE FINITE ELEMENT ANALYSIS OF NONLINEAR SLOSHING PROBLEMS BASED ON F LUID VELOCITY POTENTIAL

Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.

14000 kW救助船恶劣海况下失速系数数值研究

为研究救助船舶在恶劣海况条件下的失速性能,保证救助船舶的航行安全性,选取非线性势流计算方法和黏流CFD方法,计算KCS船在静水和规则波中的波浪增阻及船舶运动。将计算结果与船模试验数据进行对比可得:2种数值模拟计算方法在计算波浪增阻时,误差均在3.6%以内,但非线性势流理论方法相较于黏流CFD方法能够大量节约时间。因此,选定非线性势流理论计算方法为救助船数值试验计算方法,将救助船非线性势流理论计算结果与静水船模试验结果对比,在设计航速17.5 kn时,阻力误差绝对值为2.22%,选取方法有效。根据ITTC 2014年提出的失速系数计算方法进行目标船型失速预报,在设计航速17.5 kn条件下,5级海况时失速系数最大,为0.93,7级海况时失速系数最小,为0.66。

Climate Change and Its Effects on Runoff of Kaidu River, Xinjiang, China:A Multiple Time-scale Analysis

This paper applied an integrated method combining grey relation analysis, wavelet analysis and statistical analysis to study climate change and its effects on runoff of the Kaidu River at multi-time scales. Major findings are as follows: 1) Climatic factors were ranked in the order of importance to annual runoff as average annual temperature, average temperature in autumn, average temperature in winter, annual precipitation, precipitation in flood season, average temperature in summer, and average temperature in spring. The average annual temperature and annual precipi- tation were selected as the two representative factors that impact the annual runoff. 2) From the 32-year time scale, the annual runoff and the average annual temperature presented a significantly rising trend, whereas the annual precipita- tion showed little increase over the period of 1957-2002. By changing the time scale from 32-year to 4-year, we ob- served nonlinear trends with increasingly obvious oscillations for annual runoff, average annual temperature, and annual precipitation. 3) The changes of the runoff and the regional climate are closely related, indicating that the runoff change is the result of the regional climate changes. With time scales ranging from 32-year, 16-year, 8-year and to 4-year, there are highly significant linear correlations between the annual runoff and the average annual temperature and the annual precipitation.

Energy decay for a class of nonlinear wave equations with a critical potential type of damping

The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.

A nonlinear rheological model of backfill material for retaining roadways and the analysis of its stability

The long-term stability of backfill material is the key to retaining roadways successfully. In order to study the rheological deformation of backfill material and its long-term stability, given the visco-elastoplastic properties of this material, we introduced a softening and a hardening function for a new nonlinear the- ological model with time-varying parameters. Based on this, we presented the instability condition of this model by using the principle of minimum potential energy. Combined with engineering practice, we cal- culated the urlstable time period of backfill material. The results show that the time of instability of the backfill material relate to the initial parameters of the material, ＂the coefficients decided by temperature and the ratio of the plastic zone of the backfill material. Based on the results of our analysis from the point of view of energy, we can quickly obtain the time of instability of this model from our graphical analysis. The time of instability of the backfill material obtained from our investigation coincides with an actual project.

A Fully Flexible Potential Model for Carbon Dioxide

A fully flexible potential model for carbon dioxide has been developed to predict the vapor-liquid coexistence properties using the NVT-Gibbs ensemble Monte Carlo technique(GEMC).The average absolute deviation between our simulation and the literature experimental data for saturated liquid and vapor densities is 0.3% and 2.0%,respectively.Compared with the experimental data,our calculated results of critical properties(7.39 MPa,304.04 K,and 0.4679 g?cm-3) are acceptable and are better than those from the rescaling the potential parameters of elementary physical model(EPM2).The agreement of our simulated densities of supercritical carbon dioxide with the experimental data is acceptable in a wide range of pressure and temperature.The radial distribution function estimated at the supercritical conditions suggests that the carbon dioxide is a nonlinear molecule with the C O bond length of 0.117 nm and the O C O bond angle of 176.4°,which are consistent with Car-Parrinello molecular-dynamics(CPMD),whereas the EPM2 model shows large deviation at supercritical state.The predicted self-diffusion coefficients are in agreement with the experiments.

CLIMATE CHANGE:LONG-TERM TRENDS AND SHORT-TERM OSCILLATIONS

Identifying the Northern Hemisphere （NH） temperature reconstruction and instrumental data for the past 1000 years shows that climate change in the last millennium includes long-term trends and varioas oscillations. Two long-term trends and the quasi-70-year oscillation were detected in the global temperature series tbr the last 140 years and the NH millennium series. One important feature was emphasized that temperature decreases slowly but it increases rapidly based on the analysis of different series. Benefits can be obtained of climate change from understanding various long-term trends and oscillations. Millennial temperature proxies from the natural climate system and time series of nonlinear model system are used in understanding the natural climate change and recognizing potential benefits by using the method of wavelet transform analysis. The results from numerical modeling show that major oscillations contained in numerical solutions on the interdecadal timescale are consistent with that of natural proxies. It seems that these oscillations in the climate change are not directly linked with the solar radiation as an external tbrcing. This investigation may conclude that the climate variability at the interdecadal timescale strongly depends on the internal nonlinear effects in the climate system.

Approximated Vector Potential of Intense Laser Pulses in a Pair Plasma

A （3＋1 ）-dimensional Kadomtse-Petviashvili （KP） equation for nonlinearly interacting intense laser pulses with an electron-positron （e-p） plasma is derived. Taking into account the combined action of the relativistic particle mass increase and the relativistic light ponderomotive force, using the perturbation method, and allowing different types solution, we discuss the analytical solution of （3＋1）-dimensional KP-I equation, and give the approximate solutions of vector potential of the intense laser pulse in e-p plasma. Our results may be significantly useful in understanding the nonlinear wave propagation and interaction of intense laser beams in an e-p plasma.

Computing Ground State Solution of Bose-Einstein Condensates Trapped in One-Dimensional Harmonic Potential

For Bose-Einstein condensates trapped in a harmonic potential well, we present numerical results from solving the tlme-dependent nonlinear Schrolinger equation based on the Crank-Nicolson method. With this method we are able to find the ground state wave function and energy by evolving the trial initial wave function in real and imaginary time spaces, respectively. In real time space, the results are in agreement with [Phys. Rev. A 51 （1995） 4704], but the trial wave function is restricted in a very small range. On the contrary, in imaginary time space, the trial wave function can be chosen widely, moreover, the results are stable.

A Global Investigation About Hard Core Attractive Yukawa Approximation and Adhesive Hard Sphere Approximation for Structure of Colloidal Dispersion Systems

The accuracy of hard core attractive Yukawa (HCAY) potential and adhesivehard sphere (AH) potential in representing the structure factor of short range square well potentialand Asakura and Oosawa (AO) depletion potential is examined by comparing theoretical predictionswith the existing simulation data and the present numerical results from the non-linear optimizedrandom phase approximation closure for Ornstein—Zernike equation. For the case of square-well (SW)potential, it is shown that the structure factor of HCAY potential based on a recently proposedsemi-analytical expression for the radial distribution function can describe the structure factor ofSW potential with reduced well width λ ≤ 2 only if the reduced contact potential βε_(sw) ≤0.25, while the analytical expression for the structure factor of AH potential under Percus-Yevick(PY) approximation completely fails for the case of λ 】 1.2. For the case of AO depletionpotential, the domain of validity of both HCAY potential and AH potential is complementary. With theabove analysis and considering the solid-liquid transition of the AH potential with an adhesiveparameter τ below 1.31 cannot be predicted by modified weighted density approximation, the roleplayed by the HCAY potential about the mapping manipulation should not be ignored.

Effect of Time-Dependent Atomic Scattering Length on Solitons in Bose-Einstein Condensates with a Complex Potential

We consider the one-dimensional nonlinear Schrǒdinger equations that describe the dynamics of a Bose-Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrǒdinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton.

带耗散自由面势流方程的Crank-Nicolson有限差分方法数值模拟

该文建立了带耗散自由面势流方程组Crank-Nicolson有限差分方法。通过坐标变换将不规则的水槽区域变换为一个规则的正方形区域,在计算区域构造交错网格,对非线性势流方程组建立Crank-Nicolson隐格式的有限差分方法,设计了流场变量的耦合迭代的算法。数值求解了在无耗散情况下的自由面数值解与解析解的误差,数值解吻合Frandsen的解析解。数值模拟了在不同耗散系数下的自由运动,水平激励和垂直激励下的自由面波高和速度场。数值实验表明自由振动和垂直激励振动随着耗散系数的增加波高和流场速度都减小。在水平激励下的自由面波高和速度场随耗散系数的增加而减小,当波高和速度衰减到一定程度后,自由面保持稳定的波高和速度场,自由面波高出现了耗散现象。

Global Existence and Blow-up for a Dissipative Nonlinear Schrdinger Equation with Harmonic Potential

This paper is concerned with a dissipative nonlinear Schroedinger equation with a harmonic potential. By using some intricate inequalities and the argument of priori estimates, some behaviors of the solution are investigated.

Least energy solutions for semilinear Schrdinger equation with electromagnetic fields and critical growth

We study a class of semilinear SchrSdinger equation with electromagnetic fields and the nonlinearity term involving critical growth. We assume that the potential of the equation includes a parameter A and can be negative in some domain. Moreover, the potential behaves like potential well when the parameter A is large. Using variational methods combining Nehari methods, we prove that the equation has a least energy solution which, as the parameter A becomes large, localized near the bottom of the potential well. Our result is an extension of the corresponding result for the SchrSdinger equation which involves critical growth but does not involve electromagnetic fields.