On a class of singularly perturbed elliptic equations in divergence form: existence and multiplicity results

The main purpose of this paper is to study the existence of single-peaked positive solutions of the singularly perturbed elliptic equation

     

Concentrating rotaviruses from water samples using monolithic chromatographic supports

Rotaviruses are the leading cause of diarrhoea in infants around the globe and, under certain conditions they can be present in drinking water sources and systems. Ingestion of 10–100 viral particles is enough to cause disease, emphasizing the need for sensitive diagnostic methods. In this study we have optimized the concentration of rotavirus particles using methacrylate monolithic chromatographic supports. Different surface chemistries and mobile phases were tested. A strong anion exchanger and phosphate buffer (pH 7) resulted in the highest recoveries after elution of the bound virus with 1 M NaCl. Using this approach, rotavirus particles spiked in 1 l volumes of tap or river water were efficiently concentrated. The developed concentration method in combination with a real time quantitative polymerase chain reaction assay detected rotavirus concentrations as low as 100 rotavirus particles/ml.     

Solutions with spikes at the boundary for a 2D nonlinear Neumann problem with large exponent

We consider the elliptic equation −Δu+u=0 in a bounded, smooth domain Ω in R², subject to the nonlinear Neumann boundary condition . Here p>1 is a large parameter. We prove that given any integer m?1 there exist at least two families of solutions up developing exactly m peaks ξi∈∂Ω, in the sense that , as p→∞.     

Concentrating solutions in a two-dimensional elliptic problem with exponential Neumann data

We consider the elliptic equation -Δu+u=0 in a bounded, smooth domain Ω in R² subject to the nonlinear Neumann boundary condition . Here ?>0 is a small parameter. We prove that any family of solutions u_? for which ?∫_∂Ωe^u is bounded, develops up to subsequences a finite number m of peaks ξ_i∈∂Ω, in the sense that as ?→0. Reciprocally, we establish that at least two such families indeed exist for any given m?1.     

Concentration on Hopf-fibres for singularly perturbed elliptic equations

Singularly perturbed elliptic equations with superlinear nonlinearities of polynomial type are considered on an annulus in Rⁿ${\mathbb{R}}^n$, n≥4$n\ge 4$. It is shown that for small parameters there exist solutions which concentrate on manifolds of dimensions one, three and seven, which are given as Hopf-fibres.     

聚光型光伏电池冷却热管蒸发端的数值模拟

针对碟式聚光型太阳能光伏电池效率受温度制约的问题,采用两相闭式热虹吸管(重力热管)散热的方式,工质采用水.热管的蒸发端与聚光太阳能电池接触,其温度场对电池性能和热管效率影响显著.通过FLuENT建立了蒸发端底部的数学模型,计算过程中考虑热流密度、蒸汽饱和温度以及充液量对蒸发端性能的影响.计算结果表明,在聚光倍数为140...     

Singular limit for a nonlinear parabolic equation with terms concentrating on the boundary

We analyze the asymptotic behavior of the attractors of a parabolic problem when some reaction and potential terms are concentrated in a neighborhood of a portion Γ of the boundary and this neighborhood shrinks to Γ as a parameter ε goes to zero. We prove that the family of attractors is upper continuous at the ε=0.     

基于CPV 电池散热的射流冲击分形微通道换热器的结构优化

针对聚光光伏(CPV) 电池高热流密度散热问题, 本文提出了射流冲击与分形微通道散热相结合的解决方案, 对其流动和换热进行了模拟. 首先对分形微通道的分形级数进行分析, 四级相比三级分形微通道换热系数只增加了4.62% , 压降却升高了54.37% ; 接着对管道截面形状进行优化, 对圆形截面, 方形渐缩截面和扁管截面内流体的流动进行了模拟, 结果表明在换热量相近的情况下, 扁管拥有最低的压降; 随后对比分叉处倒圆角、 倒角和 Y形三种布置形状, 结果表明 Y 形布置有效地减少了内部流体的涡旋区, 能够在牺牲较少的换热面积的条件下, 将压降降低85 .51 % . 最后在相同水力直径条件下研究单个喷嘴、 均匀喷嘴阵列、 非均匀喷嘴阵列射流冲击分形微通道的换热性能, 模拟结果表明, 非均匀喷嘴阵列分形微通道拥有最佳的换热性能, 且压降降低了25 .99 % .