New integrable (2+1)- and (3+1)-dimensional sinh-Gordon equations with constant and time-dependent coefficients

In this work, we mainly address two new integrable (2+1)- and (3+1)-dimensional sinh-Gordon equations, which naturally appear in surface theory and fluid dynamics. The first equation includes constant coefficients, while the other is characterized with time-dependent coefficients. It is of further value to investigate the integrability of each model. This study puts forward a Painlevé test to reveal the Painlevé integrability. We show that the first equation passes the Painlevé test to confirm its integrability. However, the compatibility conditions of the second model with time-dependent coefficients provides the relation between these coefficients to ensure its integrability. We show that the dispersion relations of the two equations are distinct, whereas the phase shifts are identical. We apply the simplified Hirota's method where four sets of multiple soliton are derived for these equations.     

Acetylene adsorption on Si(1 0 0): A study of the role of surface steps

The focus of this study is on the adsorption of organic molecules onto steps on Si(1 0 0) and acetylene has been chosen as a show-case example. The study is based on a time-dependent quantum mechanical method and is divided into two parts. The first part has a methodological meaning and illustrates the dynamical events occurring when the molecule impinges onto the flat Si(1 0 0) surface. The second part analyzes preferred adsorption sites at steps, which are evaluated under stationary conditions from the minimization of the total energy. Adsorption-desorption events at those sites are analyzed considering temperature-activated motions obtained from the time-dependent representation. The simulation method is based on two Hamiltonians, i.e., semiempirical Hartree-Fock and Density Functional, and uses a cluster to model the exposed surface. Divergences and similarities of the properties of steps with respect to properties of the flat surface, as reported in the literature or obtained from this study, are analyzed and discussed.     

Time-dependent radiative transfer using Chapman-Enskog maximum entropy method

The time-dependent problems of radiative transfer involve a coupling between radiation and material energy fields and are nonlinear because of proposed temperature dependence of the medium characteristics in semi-infinite medium with Rayleigh anisotropic scattering. By means of the limited flux, Chapman-Enskog and maximum entropy technique the time-dependent radiative transfer equation has been solved explicitly. The maximum entropy method is used to solve the resulting differential equation for radiative energy density. The calculations are carried out for temperature (normalized dimensionless) Θ(x,τ), radiative energy density and net flux with Rayleigh and anisotropic scattering for different space at different times.     

Shortest paths in piecewise continuous time-dependent networks

We consider a shortest path problem, where the travel times on the arcs may vary with time and waiting at any node is allowed. Simple adaptations of the Dijkstra algorithm may fail to solve the problem, when discontinuities exist. We propose a new Dijkstra-like algorithm that overcomes these difficulties.     

Periodic solution to the time-inhomogeneous multi-server Poisson queue

We derive the periodic family of asymptotic distributions and the periodic moments for number in the queue for the multi-server queue with Poisson arrivals and exponential service for time-varying periodic arrival and departure rates, and time-varying periodic number of servers. The method is a straight-forward application of generating functions.     

Investigation of the starting process in a Ludwieg tube

The hypersonic Ludwieg tube Braunschweig (HLB) is a valve-controlled wind tunnel that has been designed for a Mach number of Ma = 5.9 and a Reynolds number range from 2.5 × 10⁶ up to 2.5 × 10⁷ 1/m. The intermittent working principle implies an unsteady onset of flow, which leads to a delay of the time frame suitable for measurements as well as to heat loads different from steady flow conditions. This work numerically simulates the starting process. It determines whether the onset of flow leads to a significant temperature rise in the model surface which in turn impacts results gathered during measurement time. The flow field in the HLB is numerically rebuilt for two operating points including valve opening. The non-stationary flow around a hyperboloid/flare configuration in the test section is calculated for one operating point including surface heating. For laminar flow it is found that due to the short duration of the starting process no significant model heating affects results obtained during measurement time.      

Ab initio investigation of the vibrational hyper-Raman spectra of ethylene, ethane, and dimethyl ether

The time-dependent Hartree–Fock approach is employed with the aug-cc-pVDZ or 6-311++G** basis set to simulate, in the harmonic approximation, the hyper-Raman spectra of ethylene, ethane, and dimethyl ether. Comparison with the experiment of Verdieck etal. [(1970) Chem. Phys. Lett. 7:219] is performed for ethylene and ethane. Effects of the polarization of the incident light and the detected light are studied for ethylene. Special focus is given on these vibrational normal modes that cannot be detected in IR and Raman spectroscopies.Contribution to the Jacopo Tomasi Honorary Issue     

Advanced supply chain planning with mixtures of backorders,lost sales,and lost contract

This paper investigates a supply chain system in which a supplier prepares for the selling season by building stock levels prior to the beginning of the season and shortages realized at the beginning of the season are represented as mixtures of backorders and lost sales. Backlogged items are replenished as soon as possible through an emergency procurement as opposed to waiting until the next scheduled delivery as in many continuous review scenarios, and the backorder rate is modeled as a piecewise linear function of the magnitude of the shortage. The often intangible cost associated with lost sales and customer goodwill is also quantified. In particular, the buyer and supplier are engaged in a contractual agreement and the loss of customer goodwill from the supplier’s perspective is represented as the expected cost associated with violating the conditions of the contract. The likelihood of contract cancellation is also represented as a function of the magnitude of shortage. The optimal solution is derived in closed form for the case of exponential demand distribution, and an example problem is illustrated with numerical data in order to demonstrate calculation of the optimal solution and corresponding sensitivity analysis for demand distributions in which the solution cannot be expressed in closed form.     

Quantum dynamics study of Li + HF reaction

We report rigorous quantum dynamics studies of the Li + HF reaction using the time-dependent wavepacket approach. The dynamics study is carried out on a recent ab initio potential energy surface, and state-selected reaction probabilities and cross sections are calculated up to 0.4 eV of collision energy. Many long-lived resonances (as long as 10 ps) at low collision energies (below 0.1 eV) are uncovered from the dynamics calculation. These long-lived resonances play a dominant role in the title reaction at low collision energies (below 0.1 eV). At higher energies, the direct reaction process becomes very important. The reaction probabilities from even rotational states exhibit a different energy dependence than those from odd rotational states. Our calculated integral cross section exhibits a broad maximum near the collision energy of 0.26 eV with small oscillations superimposed on the broad envelope which is reminiscent of the underlying resonance structures in reaction probabilities. The energy dependence of the present CS cross section is qualitatively different from the simple J-shifting approximation, in which a monotonic increase of cross section with collision energy was obtained. Received: 8 January 1997 / Accepted: 14 January 1997     

一维数值计算验证S散射矩阵变分表达式

一维谐振子被用来验证我们提出的S散射矩阵的含时变分表达式[北京大学学报(自然科学版), 1991, 27, 460]。结果表明, 这一S矩阵的变分表达式对于量子散射计算有很好的应用前景。