Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.     

Kinetic theories and mesoscopic models for solutions of nonhomogeneous liquid crystal polymers

We present a systematic derivation of hydrodynamic theories for nonhomogeneous nematic liquid crystal polymers (LCPs) by approximating the molecules as rigid ellipsoids, which can be either uniaxial molecules (spheroids) or biaxial ones. The short range interaction is assumed to be dominated by the excluded volume effect. Additional molecular properties with ellipsoidal molecules, e.g., a dipole–dipole interaction in extended nematics and chiral molecular structure in cholesterics, are accounted for through additional intermolecular potentials. Long-range molecular interaction is implemented through an averaged mean-field potential characterized by interaction functions. The extra elastic stress tensor is calculated using an extended virtual work principle consistent with conservation of angular momentum on the material volume, whereas the extra viscous stress is obtained by Batchelor’s volume averaging method. In the isothermal case, the theories are shown to satisfy the second law of thermodynamics, i.e., they admit positive production of entropy or energy dissipation. In the case of cholesterics, the kinetic theory reduces to the Leslie–Ericksen theory in the limit of weak translational diffusion, weak long range interaction, and weak flow.     

Experimental evidence for a reduction in electron thermal diffusion due to trapped particles

New high time resolution measurements of the electron thermal diffusion χ(e) throughout the sawtooth cycle of the Madison Symmetric Torus reversed-field pinch have been made by utilizing the enhanced capabilities of the upgraded multipoint, multipulse Thomson scattering system. These measurements are compared to the χ(e) due to magnetic diffusion predicted by using information from a new high spectral resolution zero-β nonlinear resistive magnetohydrodynamic simulation performed, for the first time, at the Lundquist number of high current Madison Symmetric Torus plasmas (S≈4×10(6)). Agreement between the measured and predicted values is found only if the reduction in thermal diffusion due to trapped particles is taken into account.     

Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

This work elaborates upon two robust models of gradient elasticity and gradient plasticity, and one gradient model of heat transfer, as originally advocated by the second author in the 1980’s. The objective is, after recalling the links between these models and existing generalized continuum theories as developed in the 1960’s and subsequently, to apply the same methodology to the case of diffusion with a view to establishing generalized transport equations. Aifantis double diffusivity and conductivity theory that provides generalized mass or heat transfer equations is compared to micromorphic-type hyper-temperature and micro-entropy proposals. The double temperature and the micromorphic thermal models are shown to lead to equations more general that Cattaneo’s. The sign of the coefficient of the second time-derivative of temperature is found to differ according to both approaches. The double temperature model contains a fourth space derivative term not present in the micromorphic models. Such generalized equations can be useful, for example, in the interpretation of recent femtosecond laser experiments on metals.     

用红外光谱法研究麦秸各层面的化学组成

本文以麦秸为例 ,用红外OMNI采样器研究了麦秸各层面红外光谱的差异 ,并进一步研究了麦草表面在不同的处理条件下 ,表面化学成分的变化规律。实验结果表明 :麦秸表面聚积着大量的SiO2 (～ 1 0 70cm- 1 ～ 80 0cm- 1 ) ,麦秸表皮层脂类物质含量高 (νCO =1 733cm- 1 )。麦秸表面的羟基 (～ 330 0cm- 1 )物质很少。麦秸的中层和内层主要是木素 ( 1 731 ,1 65 0 ,1 5 95 ,1 5 0 5 1 ,1 45 5 ,1 42 5 ,1 2 34,1 0 39和 835cm- 1 )和纤维素类物质 ( 335 0 ,2 935 ,2 85 0 ,1 65 0 ,1 45 5 ,1 430 ,1 367,1 31 7,1 1 60 ,1 0 34和 891cm- 1 )。木素的含量由外向里逐渐减少。麦秸表面的SiO2 是人造板制造中麦草不易粘接的主要原因。用热水处理后 ,表面仅有部分简单的碳水化合物和少量脂类物质溶出 ,而用NaOH处理麦草 ,可使表面的脂类物质和SiO2 溶出 ,便于人造板加工。