Random Lattice Model Research Articles

Coherence in the quasiparticle scattering by the vortex lattice in pure type-II superconductors

The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the de-Haas van-Alphen oscillations in a pure type-II superconductor is investigated within mean field,asymptotic perturbation theory. Using a 2D electron gas model it is shown that, due to a strict phase coherence in the many-particle correlation functions, the 'scattering' effect in the asymptotic limit ($\sqrt{E_F/\hbar\omega_c}\gg 1$) is much weaker than what is predicted by the random vortex lattice model proposed by Maki and Stephen, which destroys this coherence . The coherent many particle configuration is a collinear array of many particle coordinates, localized within a spatial region with size of the order of the magnetic length. The amplitude of the magnetization oscillations is sharply damped just below $% H_{c2}$ because of strong $180^{\circ}$ out of phase magnetic oscillations in the superconducting condensation energy ,which tend to cancel the normal electron oscillations. Within the ideal 2D model used it is found, however, that because of the relative smallness of the quartic and higher order terms in the expansion, the oscillations amplitude at lower fields does not really damp to zero, but only reverses sign and remains virtually undamped well below $H_{c2}$. This conclusion may be changed if disorder in the vortex lattice, or vortex lines motion will be taken into account. The reduced QP 'scattering' effect may be responsible for the apparent crossover from a strong damping of the dHvA oscillations just below $H_{c2}$ to a weaker damping at lower fields observed experimentally in several 3D superconductors.

Quasilattice equation of state for phase equilibria of polymer solutions.

An equation of state (EOS) recently proposed by the present authors based on the nonrandom lattice fluid theory was applied to correlate phase equilibrium properties of polymer solutions. The EOS requires only two molecular parameters for pure r-mers and one additional interaction energy parameter for binary systems. The molecular parameters for 12 common polymers and the binary interaction energy parameters for 17 common binary polymer solutions are presented. We found that the EOS describes quantitatively well the solvent activities and heats of mixing of various polymer solutions. The results obtained with the EOS is compared with the results obtained by such models as the random lattice model (Okada and Nose, 1981a, b), Flory theory (Flory, 1970) and the EOSs proposed by Sanchez and Lacombe (1976) and Panayiotou and Vera (1982) and UNIFAC-FV model (Oishi and Prausnitz, 1978). We believe that the result obtained to date demonstrated that the EOS can be a useful tool for practical phase equilibrium calculations of polymer solutions.

Numerical study of optical absorption in two-dimensional metal-insulator and normal-superconductor composites

We analyze a random RLC lattice model for the optical properties of a two-dimensional normal metal-insulator composite, using the Y − Δ transformation algorithm developed by Frank and Lobb. Within such a model, the surface plasmon resonances of a Drude metal-insulator composite are modeled by the ac resonances of a random resistor-inductor-capacitor (RLC) network. The real part of the effective conductance is found to show a broad surface plasmon resonance peak below and above the threshold. An effective-medium (EM) calculation is in excellent agreement with the results of the simulations. We also calculate the far-infrared absorption in a model composite of normal metal and superconductor, using a lattice model. The absorption shows a strong absorption below the superconducting energy gap. An approximate calculation based on the EMA is again in excellent agreement with these results.

炭素繊維強化積層複合材中のき裂検出法に関する研究 Ｉ 電気ポテンシャルの変化を用いたＣＦＲＰ積層材中のき裂進展量の測定

An in-service flaw detection and estimation method for CFRP composites using electrical potential drop is developed. It involves passing a constant current through composites and measuring the electrical potential, which changes as the crack advances. The resister network analysis of the random lattice model of CFRP composites shows that even in the plane normal to the fiber direction, CFRP composites can be considered as electrically homogeneous on a gross scale, i. e., on a scale of dimensions dozens of times large compared with the fibre radius. The analysis also shows that the method can detect the small increment of crack growth in CFRP composites with only a fraction of current that is required for metals. The relation between the amount of the crack growth and the potential change is expressed by a broken line composed of two straight lines. The method is applied to the delamination test of the DCB composite laminate specimen and the results are compared with the FEM solutions. The present method can provide accurate and inexpensive means for flaw detection and crack growth measurement in CFRP composite structures.

Spin and density fluctuations in disordered narrow-band superconductors

A tight-binding theory of strong-coupling superconductivity is formulated on the basis of a random lattice model with local electron-electron and contact-type electronphonon interactions. Functional-derivative technique yields a systematic deduction of the electron self-energy in terms of Coulomb repulsion, density and spin fluctuations. A novel procedure is proposed to average disordered Berk-Schrieffer-type equations. The phonon (λ ph)-, Coulombλ C-, and paramagnon (λ m)-mediated coupling parameters entering the superconductingT c are calculated for diffusive behaviour in dirty systems or alloys. The critical reduction ofT c due toλ m differs from the logarithmic singularity for a clean sample.

Ferromagnetism versus superconductivity in ramdom alloys

Magnetic, superconducting narrow-band alloys are studied within a random lattice model. Coulomb repulsion and contact-type attraction of the itinerant electrons, and the indirect exchange between local magnetic moments are taken into account. Averaging the free energy expansion in coherent potential approximation, the Ginzburg-Landau functional is derived with two biquadratically coupled order parameters. Coherent orderings and concentration-dependent critical temperatures are determined. The coefficients of theq2-terms, i.e. the stiffness and diffusion constants, involve vertex corrections due to impurity scattering. The coexistence criterion resulting from the 4th-order couplings cannot be fulfilled, referring to a first order transition between ferromagnetism and superconductivity. Tetracritical behaviour is found by including the direct exchanges between the localized spins.

Localized spin excitations in amorphous ferromagnets

Within the framework of a binary collision theory and a random lattice model the linearized equation of motion for the circular spin component S + j = S x j + i S y j was solved for an ensemble of amorphous ferromagnetic materials for two different situations: (i) originally generated, extended spinwaves. (ii) Continuous, local, external excitation of the spin S + 0 at site j = 0 in each sample. In both cases we derive solutions of the ensemble-averaged equation of motion as a function of time. It is shown that we have an exponential damping of the ensemble-averaged spinwave states, exp(-Γ t), and a localization of the ensemble-averaged excitation mode according to exp(-κ∣ R j ∣) in the case of local excitation at j = 0. The ratio Γ/κ is given by the group velocity of spinwaves in amorphous ferromagnets. Analogous results hold for phonons in amorphous materials.