SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|n-1eβ|x|2/2,β≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

Solutions of a system of forced burgers equation in terms of generalized laguerre polynomials

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|ⁿ⁻¹eβ|x|²/2,${\left|x\right|}^{n-1}{e}^{\beta {\left|x\right|}^2}/2,$, β≥0, x ∈?n$\beta \ge 0,\hspace{0.17em}x\hspace{0.17em}\in {?}^n$. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

Homopolymer and small‐molecule tracer diffusion in a gyroid matrix

Forced Rayleigh scattering was used to measure the tracer diffusion coefficients of the photochromic dye tetrathioindigo (TTI) and a 1,4‐polyisoprene (PI) homopolymer (8000 g/mol) in a poly(styrene‐b‐isoprene) (SI) diblock copolymer matrix that formed a bicontinuous gyroid microstructure. The diblock copolymer contained 63% polystyrene (PS) by volume and had a total molecular weight of 21,300 g/mol. Rheology and small‐angle X‐ray scattering confirmed that the diblock copolymer microphase‐separated into the bicontinuous gyroid over the temperature range 60–230 °C, where the sample disordered. For both the TTI and PI tracers, two distinct modes of transport were observed. The faster mode displayed a temperature dependence consistent with diffusion within a PI matrix, whereas the slower mode had a temperature dependence more similar to diffusion within PS. The fast diffusivities were both over an order of magnitude lower than in a corresponding PI homopolymer matrix. For TTI, this was attributed to the preferential selectivity of the dye for PS and, therefore, an averaging of the mobility between the PS and PI domains. The slow mode was consistent with a small fraction of the TTI dye molecules becoming trapped within the much slower PS domains. For the PI tracer, the reduction in the diffusion coefficient for the fast mode was attributed to a combination of the tortuosity of the struts, the suppression of constraint release within the diblock matrix, and additional friction due to the presence of some styrene segments within the PI domains. The inevitable presence of grain boundaries or defects within the matrix interrupted the percolation of the PI struts, thereby forcing some of the PI tracers to diffuse through PS. Consequently, the slow mode was attributed to the diffusion through these defects, where the PI diffusion was retarded by both the increased segmental friction and the thermodynamic barrier to entering the PS domains. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 843–859, 2001     

用附加动量理论分析掺气分流墩与消力池联合消能机理

用“附加动量”水跃理论分析了掺气分流墩与消力池联合应用的消能机理，用跃后水深、水跃长度或单宽水跃容积减少的百分数，估计新增消能设施的经济效益。并通过模型试验验证了消能的理论分析，计算了新增设施的消能量、跃后水深、水跃长度或单宽水跃容积减少的百分数。结果表明，采用掺气分流墩设施，可增进消力池的消能作用，并取得显著的经济效益，达到了附加动量水跃理论所预期的效果。     

带强迫项高阶中立型微分方程的振动性和非振动性

我们给出一类强迫高阶非线性中立型时滞微分方程一切解振动的充分条件.而且,也研究了一类强迫一阶中立型方程非振动解的渐近性.     

中立型抛物方程解的强迫振动性

本文讨论中立型抛物方程解的强迫振动，其中Ω是Rn中具有光滑边界Ω的有界区域，     

Forced flexural-and-torsional vibrations of a cantilever beam of constant cross section

The paper addresses the forced flexural-and-torsional vibrations of a cantilever beam of constant cross section. The relevant boundary-value problem is solved. The system of two partial differential equations of the fourth order that describes these vibrations is analyzed in a vector-function space and is subjected to an equivalent transformation to obtain one vector equation of the fourth order with two matrices as coefficients. One is an idempotent matrix; the other is a diagonal matrix. This makes it much easier to construct a Cauchy vector function as an analytic function of these matrices __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 102–114, August 2007.     

FORCED WAVE PROPAGATION IN VISCOELASTIC CABLE WITH SMALL SAG

Based on the linear viscoelastic differential constitutive law and cable structural model, the coupled longitudinal-transverse waves that propagate along a viscoelastic cable with small curvature is investigated. A mathematical model is presented that describes the three-dimensional nonlinear response of a viscoelastic cable. An asymptotic form of this model is obtained for the linear response of cables having small equilibrium curvature. The spectral relation governing the propagating waves is derived using transform methods. The spectral relation is employed in deriving a Green's function that is then used to construct solutions for in-plane response under distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves that propagate through the cable, one characterizing extension-comprehensive deformation and the other characteristic transverse deformation. Project supported by the National Natural Science Foundation of China (No. 59635140).     

大小叶盘-硬涂层阻尼结构的解析建模和振动分析

对叶片涂敷NiCoCrAlY+YSZ硬涂层,研究具有硬涂层的大小叶盘的动力学模型和振动特性,主要研究硬涂层对大小叶盘的阻尼减振性能的影响.首先,利用复模量理论和Oberst梁理论,建立了涂层大小叶盘结构的解析模型;然后,基于Gram-Schmidt法和Rayleigh-Ritz法,求解涂层大小叶盘结构的模态特性和受迫响应.结果表明:硬涂层阻尼对大小叶盘固有频率的影响很小,但能使模态损耗因子提高4倍,说明硬涂层可以有效提高大小叶盘的阻尼性能;此外,涂敷硬涂层可以有效抑制其受迫响应.     

Forced Convection with Slip-flow in a Channel or Duct Occupied by a Hyper-porous Medium Saturated by a Rarefied Gas

An analytic solution is obtained for forced convection flow in a parallel-plates channel or a circular duct occupied by a hyper-porous medium saturated with a rarefied gas in the slip-flow regime, for the case of uniform flux boundary conditions. As expected, it is found that velocity slip leads in general to increased heat transfer and temperature slip leads to reduced heat transfer.