高压下某些导电高分子色散关系的研究

利用晶格动力学方法,研究在高压下几种导电高分子具有不同晶格链时的色散关系及其曲线的变化.链间耦合作用的减弱使横波与纵波的ω差值相应增大,且在BZ边界处拉开一个间隙,这是维度作用的结果.     

All Subvarieties of ℒpq Have Finite Bases of Identities

We consider the varieties of lattice ordered groups with the identity of commutation of the nth powers of elements. We establish that every such l-variety with n=pq, where p and q are distinct prime numbers, has a finite basis of identities.     

Predicting the Mechanical Properties of Binary Blends of Immiscible Polymers

We couple a morphological study of an immiscible binary AB mixture with a micromechanical simulation to determine how the spatial distribution of the A and B domains and the interfacial region (interphase) affects the mechanical behavior of the blend. The morphological studies are conducted through a three-dimensional Cahn-Hilliard (CH) simulation. Through the CH calculations, we obtain the size and structure of the domains for different blend compositions. The output of the CH model serves as the input to the Lattice Spring Model (LSM), which consists of a three-dimensional network of springs. In particular, the location of the different phases is mapped onto the LSM lattice and the appropriate force constants are assigned to the LSM sites. A stress is applied to the LSM lattice and we calculate the elastic response of the material. We find that the local stress and strain fields are highly dependent on the morphology of the system. By integrating the morphological and mechanical models, we can isolate how modifications in the composition of the mixture affect the macroscopic behavior. Thus, we can establish how choices made in the components affect the ultimate performance of the material.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Compatibility and Marginality

We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can be used to better explain some classical phenomena in stochastic processes.     

H andH NMR Relaxation in Hydrogen-Bonded Solids Due to a Complex Motion: Classical Jumps over a Barrier and Incoherent Tunneling

Equations for the temperature dependence of proton and deuteron spin–lattice relaxation rates and second moments due to a complex motion consisting of classical jumps over a potential barrier and quantum mechanical tunneling through the barrier have been derived. Asymmetric double and triple potential wells are considered. These equations have been employed to analyze proton spin–lattice relaxation data for solid naphthazarin in the laboratory and rotating frames as a function of temperature. It is shown that tunneling plays an important role in the proton transfer dynamics of this compound.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group Aut(FVL2) of a free vector lattice FVL2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FVL2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FVL2 are amply described. Similar results are obtained for a free vector lattice FVL2 _Q 2 generated by two elements over a field of rational numbers.     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.