A new approach in modeling of constant temperature boundary condition in thermal lattice‐Boltzmann method

The lattice‐Boltzmann method is being applied to a diversity of fluid flow and heat transfer problems nowadays. Because of its microscale nature, strict attention should be paid when introducing macroscopic inputs to the model. One of the challenging issues dealing with macroscale and microscale treatment is the implementation of boundary conditions. In this regard constant‐temperature boundaries are frequently used in energy transfer problems. Such boundaries are simply modeled in Navier–Stokes based solvers, but they are not so harnessed in lattice‐Boltzmann models. One of the problems is that the calculated tangential heat flux is not zero along such boundaries in most of the previous models. In the present paper, a model has been developed, which has the capability of controlling tangential heat flux along the constant‐temperature boundaries. It aims to set the heat flux nearly zero along the boundary in midplane grid schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

EFFECTIVE SPECIFIC HEATS OF MULTI-PHASE THERMOELASTIC COMPOSITES

This paper studies the effective properties of multi-phase thermoelastic composites. Based on the Helmholtz free energy and the Gibbs free energy of individual phases, the effective elastic tensor, thermal-expansion tensor, and specific heats of the multi-phase composites are derived by means of the volume average of free-energies of these phases. Particular emphasis is placed on the derivation of new analytical expressions of effective specific heats at constant-strain and constant-stress situations, in which a modified Eshelby’s micromechanics theory is developed and the interaction between inclusions is considered. As an illustrative example, the analytical expression of the effective specific heat for a three-phase thermoelastic composite is presented.     

Slowly moving matter--wave gap soliton propagation in weak random nonlinear potential

We systematically investigate the motion of slowly moving matter--wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Gross--Pitaevskii equation.     

有机层界面对双层有机发光二极管复合效率的影响

建立了双层有机发光二极管中载流子在有机层界面复合的无序跳跃理论模型.由于有机分子材料的空间及能带结构的无序性，采用刚体模型处理有机层界面问题是不恰当的，而采用无序跳跃模型比较合理.复合效率及复合电流由载流子跳跃距离、有机层界面的有效势垒高度及该界面处的电场强度分布所决定：在双层器件ITO/α-NPD/Alq₃/Al中，当所加电压小于19.5V时，复合效率随着载流子跳跃距离的增加而增加，而大于19.5V时，复合效率随着其距离的增加而减少；复合效率随着有机层界面有效势垒高度的增加而增加； 关键词： 有机层界面 双层有机发光二极管 复合效率 有效势垒高度 无序跳跃模型     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Real‐Time Measurement of the Size Distribution of Diesel Exhaust Particles using a Portable 4‐stage Electrical Low Pressure Impactor

For this study, a 4 stage electrical low pressure impactor was designed to measure the real‐time size distribution of diesel particulate matter (DPM). For the performance evaluation, sodium chloride (NaCl) particles and dioctyl sebacate (DOS) particles were used. After evaluating the collection efficiency of each stage of the impactor, the size distributions of test particles were estimated using electrical current data and their inversion algorithm, and this was found to agree with the results obtained by a scanning mobility particle sizer (SMPS). For measurement of DPM, a common‐rail direct injection (CRDI) diesel engine, for engine speeds of 1,200 rpm and 1,500 rpm at 2.7 kgf·m, was used. Therefore, it was found that the size distribution of the DPM could be easily obtained, with the currents measured by the impactor and the data inversion algorithm, in less than 5 seconds. Furthermore, the effective density of the DPM could be obtained using the calculated results and the SMPS data.     

Non‐symmetric bent‐core mesogens with one terminal vinyl group

Two series of non‐symmetric banana‐shaped compounds, both with one alkyl and one alkenyl terminal tail, have been synthesized and studied. Both series were compared with the corresponding series with two saturated terminal alkyl tails. All the compounds have a bent central 1,3‐phenylene bis(4‐benzoyloxy)benzoate core; their mesophases were characterized by polarizing optical microscopy, differential scanning calorimetry, X‐ray diffraction and switching current response experiments. In all four series one of the terminal tails is varied from OC₈H₁₇ to OC₁₆H₃₃. The other terminal tails are OC₁₁H₂₃, O(CH₂)₉CH?=?CH₂, OC₁₀H₂₁ and O(CH₂)₈CH?=?CH₂. The short‐tailed compounds show monotropic or enantiotropic B₁ phases and the long‐tailed compounds the B₂ phase. The introduction of one terminal vinyl group slightly lowers the transition temperatures. The introduction of a second terminal vinyl group further suppresses the liquid crystalline properties. All compounds with B₂ phases have layer spacings that suggest a tilt of ～45° of the bent molecules in the layers, and their switching behaviour is antiferroelectric.     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.