磺化聚醚醚酮与壳聚糖共混制备直接甲醇燃料电池用质子交换膜

给出了不同磺化度下的磺化聚醚醚酮(SPEEK)用作质子交换膜的一系列性能,另外提出了一种新型的酸碱共混质子交换膜,其中,磺化聚醚醚酮和壳聚糖分别被选为酸性、碱性高分子电解质,并对所制备的质子交换膜的相关性能如质子传导性,甲醇渗透性,吸水率以及膜溶胀性、热稳定性等进行了表征,结果表明此种新型复合膜尽管在质子传导性能方面有所下降,阻醇性能改变不大,但是膜溶胀性和吸水率方面有了较大的改善.磺化度为71.4%的SPEEK与壳聚糖以5∶1摩尔比共混制备的质子交换膜,其性质可以与商品化的Nafion 117相媲美,有望在甲醇燃料电池中得到应用.     

On the minimum of extended dissipation in viscous nematodynamics

This paper develops the variational principle of minimum extended dissipation for slow (low Reynolds number) flows of nematic liquids as described by the five parametric Leslie–Ericksen–Parodi (LEP) constitutive equations. It is shown that the Eulers equations for minimizer of the extended dissipative functional are the Stokes equations for the LEP fluid. When the molecular (including magnetic) field is absent, the extended dissipative functional coincides with the true dissipative functional, whose Euler equations are the Stokes equations for the Ericksen fluid.     

Traveling wave solutions of harmonic heat flow

We prove the existence of a traveling wave solution of the equation in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at x ₃ = ±∞. Here u is a director field with values in The traveling wave has a singular point on the cylinder axis. Letting R→ ∞ we obtain a traveling wave defined in all space.     

Study of intrinsic anchoring in nematic liquid crystals based on modified Gruhn-Hess pair potential

A nematic liquid crystal slab composed of N molecular layers is investigated using a simple cubic lattice model, based upon the molecular pair potential which is spatially anisotropic and dependent on elastic constants of liquid crystals. A perfect nematic order is assumed in the theoretical treatment, which means the orientation of the molecular long axis coincides with the director of liquid crystal and the total free energy equals to the total interaction energy. We present a modified Gruhn-Hess model, which is relative to the splay-bend elastic constant K₁₃. Furthermore, we have studied the free nematic interfacial behavior (intrinsic anchoring) by this model in the assumption of the perfect nematic order. We find that the preferred orientation at the free interface and the intrinsic anchoring strength change with the value of modification, and that the director profile can be determined by the competition of the intrinsic anchoring with external forces present in the system. Also we simulate the intrinsic anchoring at different temperatures using Monte Carlo method and the simulation results show that the intrinsic anchoring favors planar alignment and the free interface is more disordered than the bulk.     

Nonuniqueness of the traveling wave speed for harmonic heat flow

Given any wave speed c∈R, we construct a traveling wave solution of ut=Δu+²|∇u|u in an infinitely long cylinder, which connects two locally stable and axially symmetric steady states at x₃=±∞. Here u is a director field with values in S²⊂R³: |u|=1. The traveling wave has a singular point on the cylinder axis. In view of the bistable character of the potential, the result is surprising, and it is intimately related to the nonuniqueness of the harmonic map flow itself. We show that for only one wave speed the traveling wave behaves locally, near its singular point, as a symmetric harmonic map.     

A director-field model of DNA packaging in viral capsids

The present work is concerned with the formulation of a continuum theory of viral DNA packaging based on a director field representation of the encapsidated DNA. The point values of the director field give the local direction and density of the DNA. The continuity of the DNA strand requires that the director field be divergence-free and tangent to the capsid wall. The energy of the DNA is defined as a functional of the director field which accounts for bending, torsion, and for electrostatic interactions through a density-dependent cohesive energy. The operative principle which determines the encapsidated DNA conformation is assumed to be energy minimization. We show that torsionless toroidal solenoids, consisting of planar coils contained within meridional planes and wrapped around a spool core, and fine mixtures of the solenoid and spool phase, beat the inverse spool construction.     

Influence of underlying local organisations in typical nematic phase of 6CHBT and induced nematic phase of bicomponent liquid crystalline systems 4DBT–12CB – a Fast Field Cycling NMR investigation

Variable-temperature proton magnetic relaxation dispersion (PMRD) profiles are collected in the induced nematic phases of the binary liquid crystalline mixtures composed of smectic mesogens: 5-butyl-2-(4-isothiocyanatophenyl)-1,3-dioxane (4DBT) and 4′-dodecyl-4-cyanobiphenyl (12CB) and the low viscous nematogen 4-(trans-4′-n-hexylcyclohexyl)-isothiocyanatobenzene (6CHBT), with a view to assess the influence of local organisations on the power spectrum of director fluctuation modes. Two distinct compositions of the binary mixture i.e. 50 mol% of 12CB (without a smectic phase) and 70 mol% of 12CB (with a smectic phase) are used. Fast Field Cycling nuclear magnetic resonance relaxometry is employed to measure proton spin-lattice relaxation rates (R₁) as a function of Larmor frequency (10 kHz–30 MHz). PMRD data analysis with the choice of a suitable model indicated nematic clusters of moderate size (~200 Å) found in the broad nematic region of 50 mol% 12CB, whose size is almost invariant with temperature. On the other hand, cybotactic clusters, i.e. local smectic organisations of relatively larger size (~2000–3000 Å), are observed near the nematic–smectic transition (T > T_AN) of 70 mol% 12CB. Interestingly, the shape geometry of such local organisations accessed from PMRD analysis is weakly anisotropic near T_AN, while being isotropic near T_NI for 70 mol% 12CB.     

Breather-like director reorientations in a nematic liquid crystal with nonlocal nonlinearity

The nature of nonlinear molecular deformations in a homeotropically aligned nematic liquid crystal (NLC) is presented. We start from the basic dynamical equation for the director axis of a NLC with elastic deformations and adopt space curve mapping procedure to analyze the dynamics. The NLC is governed by an integro-differential perturbed nonlocal nonlinear Schrödinger equation and we solve the same using Jacobi elliptic function method aided with symbolic computation and construct an exact solitary wave solution. In order to better understand the effect of nonlocality on the director reorientations of nematic liquid crystal, we have constructed the component forms of director axis using Darboux vector transformation. This intriguing property as a result of the relation between the coherence of the breather-like solitary deformation and the nonlocality reveals a strong need for a deeper understanding in the theory of self-localization in NLC systems.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists