Integrability of the Gross-Pitaevskii equation with Feshbach resonance management

In this Letter we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential. By using WTC test, we find a condition under which the Gross-Pitaevskii equation is completely integrable. Under the present model, this integrability condition is completely consistent with that proposed by Serkin, Hasegawa, and Belyaeva [V.N. Serkin, A. Hasegawa, T.L. Belyaeva, Phys. Rev. Lett. 98 (2007) 074102]. Furthermore, this integrability can also be explicitly shown by a transformation, which can convert the Gross-Pitaevskii equation into the well-known standard nonlinear Schrödinger equation. By this transformation, each exact solution of the standard nonlinear Schrödinger equation can be converted into that of the Gross-Pitaevskii equation, which builds a systematical connection between the canonical solitons and the so-called nonautonomous ones. The finding of this transformation has a significant contribution to understanding the essential properties of the nonautonomous solitons and the dynamics of the Bose-Einstein condensates by using the Feshbach resonance technique.     

Time-dependent analytical model of thermal effects in continuous-wave end-pumped Tm:YAP lasers

A time-dependent analytical thermal model of temperature and stresses is developed to investigate the transient behavior of thermal effects in continuous-wave (CW) end-pumped laser rods. To validate the model, it is applied to a CW pumped Tm:YAP crystal and found to be in very good agreement with results of solving heat-transfer equation by finite-difference method and experimental results. The temperature contribution coefficient and stress contribution coefficient are derived from the analytical model. The temperature contribution coefficients obtained from analytical and numerical models are 1.29 K/W and 1.14 K/W, respectively. For the stress contribution coefficient of 0.34 MPa/W, the permissible maximum pump power of ∼471 W is obtained. The focal lengths of the Tm:YAP is measured in the range of 40∼90 mm, when the pump power is between 16 and 34 W.     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.     

从简单模型入手探究陀螺仪在磁场中的减速问题

2019年中国大学生物理学术竞赛中,非铁磁性导体材料制的陀螺仪在磁场中减速问题的研究没有限定任何具体参数,不易根据麦克斯韦方程得到全面统一的答案.本文从无限长导体圆柱模型入手,通过合理的近似,推导得到了陀螺仪转轴与磁场方向垂直和平行两种条件下,电磁阻力矩与磁感应强度、角速度、电导率等参数依赖关系的表达式,进而给出了磁场...     

Simple formulae giving the temperature profiles in the stripe-geometry laser diodes with oxide barriers

Simple, approximate formulae describing the temperature distribution in the stripe-geometry laser diode with oxide barriers has been derived in this work. A two-dimensional, heat-spreading model has been used in which the lateral heat spreading as well as the radiative transfer of spontaneous radiation has been taken into account. The resultant formulae have been obtained using the electrical analogue of the heat flow process.     

Time-dependent thermodynamic properties of the Ising model from damage spreading

The relationship between damage spreading and static thermodynamic properties in the Ising model developed by Coniglioet al. is here extended to include time-dependent thermodynamic quantities. We exploit this new result to measure the time-dependent spin correlation function from damage spreading in the Ising model with heat bath and Glauber dynamics. Until now, only static thermodynamic quantities have been correctly determined from damage spreading, and even then, only with heat bath dynamics. We also show that there are significant differences between the kinetics of damage spreading as found in heat bath and Glauber dynamics.     

Thermodynamics of superspreading

A simple model for calculation of the spreading coefficient of an aqueous surfactant solution on an apolar solid is proposed. The spreading coefficient is predicted to have two components: i) the van der Waals component, which is similar to the spreading coefficient of the alkane, making up the surfactant tail; and ii) the monolayer frustration component, dependent on the bending moduli and the spontaneous curvature of the surfactant. The frustration term is minimized at a negative spontaneous curvature. In order for a solution to spread, the van der Waals component of the spreading coefficient must be positive and larger than the monolayer frustration term. The spreading is facilitated by surfactants having very short and branched alkyl tails. Received 19 May 1999 and Received in final form 29 October 1999     

Theoretical ROVibrational Energies (TROVE): A robust numerical approach to the calculation of rovibrational energies for polyatomic molecules

We present a new computational method with associated computer program TROVE (Theoretical ROVibrational Energies) to perform variational calculations of rovibrational energies for general polyatomic molecules of arbitrary structure in isolated electronic states. The (approximate) nuclear kinetic energy operator is represented as an expansion in terms of internal coordinates. The main feature of the computational scheme is a numerical construction of the kinetic energy operator, which is an integral part of the computation process. Thus the scheme is self-contained, i.e., it requires no analytical pre-derivation of the kinetic energy operator. It is also general, since it can be used in connection with any internal coordinates. The method represents an extension of our model for pyramidal XY₃ molecules reported previously [S.N. Yurchenko, M. Carvajal, P. Jensen, H. Lin, J.J. Zheng, W. Thiel, Mol. Phys. 103 (2005) 359]. Non-rigid molecules are treated in the Hougen-Bunker-Johns approach [J.T. Hougen, P.R. Bunker, J.W.C. Johns, J. Mol. Spectrosc. 34 (1970) 136]. In this case, the variational calculations employ a numerical finite basis representation for the large-amplitude motion using basis functions that are generated by Numerov-Cooley integration of the appropriate one-dimensional Schrödinger equation.     

用PM3量化参数预测多氯代二苯并呋喃的logKow

从现有的PCDFs分子的正辛醇 /水分配系数 (logKow)实验数据出发 ,建立定量结构 性质关系方程(QSPR) .采用G98W程序包中的PM3方法对 13 5个多氯代二苯并呋喃 (PCDFs)分子和二苯并呋喃进行了优化计算 ,作业命令为 #pPM3optfreqscf(conver =9) ,以计算所得的分子轨道能量、碳原子电荷作为PCDFs分子结构描述符 ,运用多元线性回归技术建立了PCDFs的logKow与分子结构描述符的四元方程 ,最优相关系数为 0 .95 0 7,标准偏差为 0 .173 7,经检验该模型的稳健性好 ,并对未有实验数据的 85个PCDFs的logKow进行预测     

Quantenstatistische Zustandsgleichung von stark ionisierten Wasserstoffplasmen mittlerer Dichte

A quantum statistical formula for the equation of state of fully ionized plasmas in the mean temperature and mean density region is given. The complete second virial coefficient for the case of Debye screening is taken into account. The binary Slater sums are represented by interpolation between the analytical expressions for small and for large radii respectively. Using the interpolation formulae the equation of state is calculated numerically for the temperatures T = 20000 K and T = 80000 K. The resulting curves are in good agreement with the analytical equation of state for very small densities.     

折射率与电声子相互作用的关系

从微观出发研究电声子相互作用对折射率的影响。用半经典方法导出一个适用于晶态和无序度小的介质折射率公式和折射率温度系数公式。首次指出电声子相互作用引起的折射率温度系数,高温时为一常数,低温时与T~3成正比。并与实验作了对比,理论曲线与实验符合得很好。用得到的公式计算了好几种材料的温度系数。计算值与实验值相符合。     

The Symmetry Structure of the Heavenly Equation

We show that excitations of physical interest for the heavenly equation are generated by symmetry operators which yield two reduced equations with different characteristics. One equation is of the Liouville type and gives rise to gravitational instantons, including those found by Eguchi–Hanson and Gibbons–Hawking. The second equation appears for the first time in the theory of heavenly spaces and provides meron-like configurations endowed with a fractional topological charge. A link is also established between the heavenly equation and the so-called Schröder equation, which plays a crucial role in the bootstrap model and in renormalization theory.     

A kinetic modeling study on the oxidation of primary reference fuel-toluene mixtures including cross reactions between aromatics and aliphatics

A detailed chemical kinetic model for the mixtures of primary reference fuel (PRF: n-heptane and iso-octane) and toluene has been proposed. This model is divided into three parts; a PRF mechanism [T. Ogura, Y. Sakai, A. Miyoshi, M. Koshi, P. Dagaut, Energy Fuels 21 (2007) 3233-3239], toluene sub-mechanism and cross reactions between PRF and toluene. Toluene sub-mechanism includes the low temperature kinetics relevant to engine conditions. A chemical kinetic mechanism proposed by Pitz et al. [W.J. Pitz, R. Seiser, J.W. Bozzelli, et al., in: Chemical Kinetic Characterization of the Combustion of Toluene, Proceedings of the Second Joint Meeting of the U.S. Sections of the Combustion Institute, 2001] was used as a starting model and modified by updating rate coefficients. Theoretical estimations of rate coefficients were performed for toluene and benzyl radical reactions important at low temperatures. Cross reactions between alkane, alkene, and aromatics were also included in order to account for the acceleration by the addition of toluene into iso-octane recently found in the shock tube study of the ignition delay [Y. Sakai, H. Ozawa, T. Ogura, A. Miyoshi, M. Koshi, W.J. Pitz, Effects of Toluene Addition to Primary Reference Fuel at High Temperature, SAE 2007-01-4104, 2007]. Validations of the model were performed with existing shock tube and flow tube data. The model well predicts the ignition characteristics of PRF/toluene mixtures under the wide range of temperatures (500-1700 K) and pressures (2-50 atm). It is found that reactions of benzyl radical with oxygen molecule determine the reactivity of toluene at low temperature. Although the effect of toluene addition to iso-octane is not fully resolved, the reactions of alkene with benzyl radical have the possibility to account for the kinetic interactions between PRF and toluene.     

Analysis of EPR-time profiles of transient radicals with unresolved spectra

A method for analysing EPR-time profiles of transient radicals in solution with unresolved hyperfine structure is proposed. It is based on considering the magnetic field integral of the magnetization, i.e., the total EPR signal intensity, instead of single components of overlapping EPR transitions. For a radical system involving chemical kinetics, chemically induced electron polarization (CIDEP), and spin relaxation, an analytical solution is found for the evolution of the integral magnetization in the Laplace domain. The solution in the time domain is given for the case of negligible saturation, i.e., omega2(1)T1T2 < 1. The formulae presented are suitable to avoid equivocal multi-parameter fits when analysing the results of time-resolved continuous-wave EPR experiments for the observables, which characterize the chemical kinetics, CIDEP, and electron spin relaxation of radical systems.     

Temperature effects on optical properties of InN thin films

Transmission measurements have been carried out on InN thin films grown by radio frequency magnetron sputtering on a sapphire (0001) substrate at 10–300 K. With the aid of a novel procedure developed for analyzing the transmission spectra, the effect of temperature on optical properties, such as the absorption coefficient, band-gap, Urbach bandtail characteristics, refractive index and extinction coefficient, of InN thin films has been determined. The wavelength and temperature dependence of the absorption coefficient in both the Urbach and intrinsic absorption regions has been described by a series of empirical formulae. The temperature dependence of the refractive index dispersion below the band-gap is also found to follow a Sellmeier equation. These formulae are very useful for the characterization and device design of InN films. The free-electron concentration in the InN thin film determined here is also found to be in good agreement with that obtained from infrared reflection measurements. PACS 78.66.Fd; 78.40.Fy; 78.20.Bh; 78.20.Ci     

Mathematical simulation of heat and mass transfer in a cylindrical channel versus the tangential momentum accommodation coefficient

The process of heat and mass transfer in a long cylindrical channel has been considered in terms of the mirror–diffuse model of the Maxwell boundary condition. The Hazen–Williams equation is used as a basic equation of the process kinetics. A constant temperature gradient is maintained in the channel. The heat and mass fluxes through the cross section of the channel versus the tangential momentum accommodation coefficient have been calculated in a wide range of the Knudsen number. The heat flux profiles have been constructed. A comparison with relevant published data has been carried out.     

量子环中量子比特的消相干时间

在量子环中电子与体纵光学声子强耦合的情况下,通过求解能量本征方程,得出了电子的基态和第一激发态的本征能量及其波函数,进而以电子-声子体系的基态与第一激发态构造一个量子比特.结果讨论了消相干时间与耦合强度,色散系数以及量子环内径、外径的变化关系.     

Direct measurement of the W Boson width in ppover collisions at square roots = 1.96 TeV

A direct measurement of the total decay width of the W boson Gamma(W) is presented using 350 pb(-1) of data from pp[over ] collisions at square root s = 1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. The width is determined by normalizing predicted signal and background distributions to 230 185 W candidates decaying to enu and micronu in the transverse-mass region 50相似文献   

Phase diagram of the Gross-Neveu model: exact results and condensed matter precursors

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1 + 1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schrödinger equation with the (single gap) Lamé potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Fröhlich model and ferromagnetic superconductors.