Quadrature in Besov spaces on the Euclidean sphere

Let q1 be an integer, denote the unit sphere embedded in the Euclidean space , and μ_q be its Lebesgue surface measure. We establish upper and lower bounds for

where is the unit ball of a suitable Besov space on the sphere. The upper bounds are obtained for choices of x_k and w_k that admit exact quadrature for spherical polynomials of a given degree, and satisfy a certain continuity condition; the lower bounds are obtained for the infimum of the above quantity over all choices of x_k and w_k. Since the upper and lower bounds agree with respect to order, the complexity of quadrature in Besov spaces on the sphere is thereby established.     

Ancestral population genomics using coalescence hidden Markov models and heuristic optimisation algorithms

With full genome data from several closely related species now readily available, we have the ultimate data for demographic inference. Exploiting these full genomes, however, requires models that can explicitly model recombination along alignments of full chromosomal length. Over the last decade a class of models, based on the sequential Markov coalescence model combined with hidden Markov models, has been developed and used to make inference in simple demographic scenarios. To move forward to more complex demographic modelling we need better and more automated ways of specifying these models and efficient optimisation algorithms for inferring the parameters in complex and often high-dimensional models.In this paper we present a framework for building such coalescence hidden Markov models for pairwise alignments and present results for using heuristic optimisation algorithms for parameter estimation. We show that we can build more complex demographic models than our previous frameworks and that we obtain more accurate parameter estimates using heuristic optimisation algorithms than when using our previous gradient based approaches.Our new framework provides a flexible way of constructing coalescence hidden Markov models almost automatically. While estimating parameters in more complex models is still challenging we show that using heuristic optimisation algorithms we still get a fairly good accuracy.     

土壤覆盖条件下水,汽,热运动的数值模拟

本文建立了一种使用交替方向隐式有限差分法（ＡＤＩ）来研究条带状覆盖情况下二维土壤水热流动的计算模型，该模型使用土壤表面能量平衡方程来确定热和水流的土壤表面的边界条件，讨论了模型中所需要输入的参数，并且经ＣｈｕｎｇＳ－Ｏ等人试验进行了验证，为评价地下水资源量提供可靠的依据。     

The numerical simulation of two-dimensional aluminized composite solid propellent combustion

A numerical framework is presented which examines, for the first time, the burning of two-dimensional aluminized solid propellants. Aluminized composite propellants present a difficult mathematical and numerical challenge because of complex physics and topological changes that occur at the propellant surface. For example, both mathematical models and appropriate numerical solvers must describe the regressing burning surface, aluminium particle detachment and evolution throughout the gas-phase flow field, surface tension effects, ignition and combustion of aluminium particles, phase change effects, agglomeration of aluminium particles, radiation feedback to the propellant surface, to name a few. All of these effects must be modelled in a consistent manner. A numerical framework for which these effects can be included in a rational fashion is currently being developed. This framework includes the level set method to capture the solid–gas interface as well as particle motion in the gas phase. Some preliminary calculations of the two-dimensional combustion field supported by a disc pack with embedded aluminium particles are presented.     

一种耦合斯特林制冷效应的复合式磁制冷循环的数值模拟

介绍了一种斯特林回热式制冷效应和主动式磁制冷效应耦合的新型制冷循环。循环采用的回热填料钆既是磁制冷循环的磁热材料又是斯特林制冷的回热材料。通过斯特林回热式制冷循环和磁制冷效应的正面耦合叠加获得更优良的制冷效果。同时介绍了一种磁制冷回热器的数值计算模型,本模型是基于控制容积法计算的一维交变流动模型,并对常规回热器内填料能量控制方程进行了修正,考虑了磁性材料磁热效应的影响,添加内热源项。论文计算分析了系统相位角、压力和频率的变化对制冷性能的影响。文中给出的部分模拟结果对后续实验台的改造有一定的借鉴指导作用。     

Sequential evaluation of continuous deformation field of semi-crystalline polymers during tensile deformation accompanied by neck propagation

The localized deformation field of high density polyethylene and polypropylene during a tensile test accompanied by neck propagation was quantitatively evaluated based on the network digital image correlation method. In the proposed method, the continuity of the deformation field around a point of interest was introduced for accurate evaluation of the displacement. The accuracy of the proposed method was verified through test images. Using the proposed method, the development of a non-uniform displacement field during tensile tests was evaluated from sequential digital images. The local strain rate was almost uniform until the nominal stress reached its maximum value. After the maximum stress was reached, non-uniform deformation developed at a part of the gauge region of the specimen. A decrease in nominal stress induced a reduction of the local strain rate at regions other than the necked zone. In this study, the cross section average local true stress, strain, and strain rate can be evaluated from the local displacement field. Thus, the relationship between these quantities was evaluated during the tensile tests. Using the proposed method, the local response under wide ranges of strain and strain rate can be evaluated from a few test conditions of tensile strain rate and a small range of tensile strain. Finally, the relationships between gradients of stress, strain, and strain rate under uniaxial tension are discussed. These non-local quantities deviated from those predicted by constitutive equations when the domain size used to evaluate the local quantities was large.     

Interstitial fluid flow: simulation of mechanical environment of cells in the interosseous membrane

In vitro experiments have shown that subtle fluid flow environment plays a significant role in living biological tissues,while there is no in vivo practical dynamical measurement of the interstitial fluid flow velocity.On the basis of a new finding that capillaries and collagen fibrils in the interosseous membrane form a parallel array,we set up a porous media model simulating the flow field with FLUENT software,studied the shear stress on interstitial cells’ surface due to the interstitial fluid flow,and analyzed the effect of flow on protein space distribution around the cells.The numerical simulation results show that the parallel nature of capillaries could lead to directional interstitial fluid flow in the direction of capillaries.Interstitial fluid flow would induce shear stress on the membrane of interstitial cells,up to 30 Pa or so,which reaches or exceeds the threshold values of cells’ biological response observed in vitro.Interstitial fluid flow would induce nonuniform spacial distribution of secretion protein of mast cells.Shear tress on cells could be affected by capillary parameters such as the distance between the adjacent capillaries,blood pressure and the permeability coefficient of capillary’s wall.The interstitial pressure and the interstitial porosity could also affect the shear stress on cells.In conclusion,numerical simulation provides an effective way for in vivo dynamic interstitial velocity research,helps to set up the vivid subtle interstitial flow environment of cells,and is beneficial to understanding the physiological functions of interstitial fluid flow.     

Dynamics of dual pontoon floating structure for cage aquaculture in a two-dimensional numerical wave tank

The trend of using floating structures with cage aquaculture is becoming more popular in the open sea. The purpose of this paper is to investigate the dynamic properties of a dual pontoon floating structure (DPFS) when attached to a fish net by using physical and numerical models. A two-dimensional (2-D) fully nonlinear numerical wave tank (NWT), based on the boundary element method (BEM), is developed to calculate the wave forces on the DPFS. The wave forces on a fish net system are then evaluated using a modified Morison equation. The comparisons of dynamic behaviors between numerical simulations and experimental measurements on the DPFS show good agreement. Results also display that a fish net system causes the resonant response of body motions and mooring forces to be slightly lower due to the net's damping effect. Finally, for designing the rearing space of cage aquaculture, the influences which net depth and net width have on the DPFS dynamic responses are also presented in this paper.     

Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder close to a plane boundary are investigated numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the Arbitrary Lagrangian Eulerian (ALE) scheme with a k-ω turbulence model closure. The numerical model is validated against experimental data of VIV of a cylinder in uniform flow and VIV of a cylinder close to a plane boundary at low mass ratios. The numerical results of the vibration mode, vibration amplitude and frequency agree well with the experimental data. VIV of a circular cylinder close to a plane boundary is simulated with a mass ratio of 2.6 and gap ratios of e/D=0.002 and 0.3 (gap ratio is defined as the ratio of gap between the cylinder and the bed (e) to cylinder diameter (D)). Simulations are carried out for reduced velocities ranging from 1 to 15 and Reynolds numbers ranging from 1000 to 15 000. It is found that vortex-induced vibrations occur even if the initial gap ratio is as small as e/D=0.002, although reported research indicated that vortex shedding behind a fixed circular cylinder is suppressed at small gap ratios (e/D<0.3 or 0.2). It was also found that vibration amplitudes are dependant on the bouncing back coefficient when the cylinder hits the plane boundary. Three vortex shedding modes are identified according to the numerical results: (i) single-vortex mode where the vortices are only shed from the top of the cylinder; (ii) vortex-shedding-after-bounce-back mode; (iii) vortex-shedding-before-bounce-back mode. It was found that the vortex shedding mode depends on the reduced velocity.     

Effects of supply air temperature and inlet location on particle dispersion in displacement ventilation rooms

The effects of supply temperature and vertical location of inlet air on particle dispersion in a displacement ventilated (DV) room were numerically modeled with validation by experimental data from the literature. The results indicate that the temperature and vertical location of inlet supply air did not greatly affect the air distribution in the upper parts of a DV room, but could significantly influence the airflow pattern in the lower parts of the room, thus affecting the indoor air quality with contaminant sources located at the lower level, such as particles from working activities in an office. The numerical results also show that the inlet location would slightly influence the relative ventilation efficiency for the same air supply volume, but particle concentration in the breathing zone would be slightly lower with a low horizontal wall slot than a rectangular diffuser. Comparison of the results for two different supply temperatures in a DV room shows that, although lower supply temperature means less incoming air volume, since the indoor flow is mainly driven by buoyancy, lower supply temperature air could more efficiently remove passive sources (such as particles released from work activities in an office). However, in the breathing zone it gives higher concentration as compared to higher supply air temperature. To obtain good indoor air quality, low supply air temperature should be avoided because concentration in the breathing zone has a stronger and more direct impact on human health.