A Hunziker-van Winter-Zhislin theorem for a four-particle lattice Schrödinger operator

We consider a discrete Schrödinger operator for four arbitrary particles with short-range pair potentials. We describe the position and the structure of its essential spectrum and prove the Hunziker-van Winter-Zhislin theorem.     

Finite element modelling of surface waves in a channel

A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms.     

Experimental investigation on the flame front resistance of gas channel growth with melt formation in iron ore sinter beds

The resistance of the flame front within the solid bed constitutes a fundamental and crucial area in porous bed combustion as the flame front propagation is highly related to the productivity and product quality. This paper focuses on the iron ore sintering, a thermal agglomeration process in steel mills. The results from a detailed experimental study of the pilot-scale pot tests under the conditions of a wide range of fuel rate are presented. The primary objective is to provide better understanding of the growth of gas channels relating to melt formation in the flame front and its resistance to flow. The sintering bed was divided into several zones based on the temperature profile and component distribution. Even though there is a continuous one-to-one replacement of humidified zone with porous sintered zone, a constant air flow rate during sintering could be obtained, indicating the ～100?mm high-temperature zone has a controlling effect on sintering bed permeability. The specific pressure drop value in high-temperature zone increases from ～3?kPa in upper bed to ～7?kPa in bottom bed, which varies with the bed temperature and structure properties. Both the green bed and sintered bed were scanned by X-ray computed tomography, the reconstruction and image analysis showed that the sintered bed has large gas channels and many more closed pores due to solid-melt-gas coalescence. More melt is generated when the heat is accumulated along the bed or input higher coke content, showing a propensity to suppress the gas channel growth and amplify the mismatch of gas transportation along the bed. Higher coke rate leads to a higher resistance in flame front, resulting in a slower flame front speed. These results are aimed to provide quantitative validation for improvements of a numerical sintering model in a future work.     

The effects of different dispersion compensation ratios on nonlinear single channel and WDM systems

The effects of the compensation ratio with dispersion post-compensation on nonlinear single channel and WDM systems with 10 Gb/s per channel are numerically investigated. When the transmission signal per channel is 10 Gb/s RZ pulse and the amplifier span is 50 km, proper undercompensation can enhance the performance of the nonlinear single channel system and the nonlinear WDM system. But the enhanced distance of the nonlinear WDM system is not as obvious as that of the single channel system, because the cross-phase-modulation effect plays an important role in the nonlinear WDM system.     

Layouts for mobility management in wireless ATM networks

In this paper, we present a new model that combines quality of service and mobility aspects in wireless ATM networks. Namely, besides the hop count and load parameters of the basic ATM layouts, we introduce a new notion of distance that estimates the time needed to reconstruct the virtual channel of a wireless user when he moves through the network. Quality of service guarantee dictates that the rerouting phase must be imperceptible, that is, the maximum distance between two virtual channels must be maintained as low as possible. Therefore, a natural combinatorial problem arises in which suitable trade-offs must be determined between the different performance measures. We first show that establishing the existence of a layout with maximum hop count h, load l and distance d is NP-complete, even in the very restricted case h=2, l=1 and d=1. We then provide optimal layout constructions for basic interconnection networks, such as chains and rings.     

A size-modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage-dependent anion channel

We present a new size-modified Poisson–Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage-dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc.