An example of cycling in a feasible point algorithm

An example shows that, if in Rosen's [4] algorithm for calculating a point that satisfies linear constraints a natural criterion is used to select constraints to delete from active sets, then the algorithm may cycle instead of converging. There are no degeneracies in the example.     

Trends in microdisk laser research and linear optical modelling

Research into microdisk lasers demonstrates new achievements both in the technology and in the associated physical effects and applications. Melting and rounding of the disk edge boosts the Q-factors due to improved surface smoothness. In-plane cavity shape is widely used as a design instrument. Optimal shaping of pumped area lowers the threshold power. Photonic molecules made of several microdisks as “photonic atoms” show lasing at several closely spaced frequencies. A microdisk with a single quantum dot as an active region is considered as the most promising system for realisation of a single photon emitter necessary for quantum computing. These new effects and devices can be simulated with accurate numerical techniques, developed recently for “warm-cavity” linear modelling, that are able to bring a new vision of the physics of lasing.     

Understanding periodically twinned structure in nano-wires

Using first-principles calculations we have investigated the high stability of twinned nano-wires, which explains why the stacking faults always appear. Furthermore, we present a growth model to describe the formation mechanism of the stacking faults in the compound nano-wire with zinc-blende structure (e.g. SiC). And the model is confirmed by the numerical calculation based on the point charge approximation.     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.     

Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot

The electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s–1p, 1p–1d and 1d–1f transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states.     

Beam quality factor of mixed modes emerging from a multimode step-index fiber

The beam quality factors (or M² parameter) of coherent and incoherent superposition of the several lower-order LP modes emerging from a step-index fiber have been calculated by using the second-order moment method. The results indicate that, for an individual LP mode, the M² parameter takes its maximum value when the normalized frequency V of the step-index fiber approaches the cut-off frequency, and it gradually becomes constant as V increases. In the case of incoherent superposition, the larger the fraction intensity carried by the higher-order mode, the larger the beam quality factor M². Under certain circumstances, the value of the M² parameter of the mixed mode that comprises several LP-modes contents may become even smaller and closer to the ideal Gaussian beam than that of the fundamental mode in a step-index fiber. However, in the case of the coherent superposition, the value of the M² parameter of the mixed mode may be greater than that of the higher-order constituent mode. The results reported here could be helpful for the application of the high-power fiber laser systems.     

Importance of Darcy–Forchheimer porous medium in 3D convective flow of carbon nanotubes

This article explores Darcy–Forchheimer 3D flow of water-based carbon nanomaterial (CNTs). A bi-directional linear stretchable surface has been used to create the flow. Flow in porous space is represented by Darcy–Forchheimer expression. Heat transfer mechanism is explored through convective heating. Results for single-wall (SWCNTs) and multi-wall (MWCNTs) carbon nanotubes have been presented and compared. The reduction of partial differential system into nonlinear ordinary differential system is made through suitable variables. Optimal homotopic scheme is used for solutions development of governing flow problem. Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables. Skin friction coefficients and local Nusselt number are analyzed through plots. Our findings show that the skin friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.     

A competitive (dual) simplex method for the assignment problem

Where there is abundance of mystery and confusion in every direction, the truth seldom remains hidden for long. It's a matter of having plenty of angles to go at it from. Only the utterly simple crimes - the simplex crimes, you may say - have the trick of remaining baffling. - Sir John (from Michael Innes,The Open House (A Sir John Appleby Mystery), Penguin Books, 1974).A dual simplex method for the assignment problem leaves open to choice the activity (i,j) of rowi and columnj that is to be dropped in pivoting so long asx _ij < 0. A choice (i,j) over columnsj having at least 3 basic activities that minimizesx _ij is shown to converge in at most ( ₂ ^n-1 ) pivots, and at most O(n ³) time, and it is argued that on average the number of pivots is at mostn logn. Dedicated with affection to George B. Dantzig on the occasion of his seventieth birthday.     

聚甲基丙烯酸甲酯-丙烯酸酰胺嵌段共聚物的合成与表征

引发剂;苯胺;聚甲基丙烯酸甲酯-丙烯酸酰胺嵌段共聚物的合成与表征     

基于分子内旋转受限原理的线性共轭小分子的AIE性能研究

研究了6个线性共轭化合物4-丁基联苯(L1)、4,4’-二异丙基联苯(L2)、5,5’-二甲基-2,2’-联吡啶(L3)、2-([1,1’-联苯]-4-)噻吩(L4)、1,1’-联萘(L5)和5-苯基-2,2’-联噻吩(L6)的紫外-可见光谱和荧光发射光谱。结果表明,化合物L1、L2和L3均具有聚集诱导发光(AIE)性能,化合物L4、L5和L6则不具有AIE性能。该研究结果表明,二联苯(或两个简单芳杂环相连)系列化合物具有AIE性能,分子内旋转受限(RIR)是该系化合物产生AIE现象的机理。但是在二联苯的结构基础上继续增加链的长度,或者引入体积更大的芳环(萘环),化合物不再具有AIE性能。