Extension of the Coherent Gradient Sensor (CGS) to the Combined Measurement of In-Plane and Out-of-Plane Displacement Field Gradients

The Coherent Gradient Sensor (CGS) is extended to the optical differentiation of specular, diffracted wave fronts leading to the combined measurement of in- and out-of-plane displacement field gradients. A derivation of the underlying optical interference principles is presented along with an analysis of the effective instrument sensitivity. In order to demonstrate the capabilities of the technique, experimental measurements of crack-tip deformation fields were conducted under various loading conditions corresponding to mode-I, mode-II, and mixed mode near-tip crack fields. The experimental procedures and results of these tests are presented as validation of the technique.     

Gribov ambiguity in gauge theories

Gribov ambiguity in gauge field theories is discussed and it is shown that such an ambiguity exists even for Abelian theories in covariant gauge at finite temperature. Both geometric and algebraic proofs are presented. In view of the importance of non-perturbative methods, some special gauges are given in which such ambiguities do not exist or are not relevant. The significance of these in the study of confinement in QCD is pointed out.     

On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative ∂u of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group.     

High performance polymer field‐effect transistors based on polythiophene derivative with conjugated side chain

Poly(3‐[2‐(5‐hexyl‐2‐thienyl) ethenyl]‐2,2′‐bithiophene) ( P2 , see Scheme 1 ) with conjugated thienylvinyl side chain was synthesized by copolymerization of the thiophene units with and without conjugated side chain with Pd‐catalyzed Stille coupling method. For comparison, P1 with the hexyl side chain instead of conjugated side chain was also synthesized. P2 film shows broad absorption in the visible region with absorption edge at about 700 nm. The solution‐processed polymer field‐effect transistors were fabricated and characterized with bottom gate/top contact geometry. The organic field‐effect transistors (OFET) based on P2 showed an average hole mobility of about 0.034 cm²/Vs (the highest value reached 0.061 cm²/Vs) upon annealing at about 180 °C for 30 min, with a threshold voltage of ?1.15 V and an on/off ratio of 10⁴ with n‐octadecyltrichlorosilane (OTS) modified SiO₂ substrate. In comparison, the OFET based on P1 displayed a hole mobility of 8.9 × 10^–4 cm²/Vs and an on/off ratio of 10⁴ with OTS modified SiO₂ substrate. The results indicate that the polythiophene derivative with conjugated thienylvinyl side chain is a promising polymer for the application in polymer field‐effect transistors. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5304–5312, 2009     

Laplaza sets, or how to select coherence diagrams for pseudo algebras

We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such a notion was introduced in [Po Hu, Igor Kriz, Conformal field theory and elliptic cohomology, Adv. Math. 189 (2) (2004) 325-412, http://www.math.lsa.umich.edu/~ikriz/], but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, allowing more flexibility in selecting coherence diagrams for pseudo algebras.     

Quadratic Actions in Dependent Fields and the Action Principle

General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities L _I (x;λ), with λ a generic coupling constant, such that the following expression ∂ L _I (x;λ)/∂ λ may be expressed as quadratic functions in dependent fields but may, in general, be arbitrary functions of independent fields. These necessarily include, as special cases, present renormalizable gauge theories. It is shown, in a unified manner, that the vacuum-to-vacuum transition amplitude (the generating functional) may be explicitly derived in functional differential form which, in general, leads to modifications to computational rules by including such factors as Faddeev–Popov ones and modifications thereof which are explicitly obtained. The derivation is given in the presence of external sources and does not rely on any symmetry and invariance arguments as is often done in gauge theories and no appeal is made to path integrals.     

ARC INTERFACE CRACK IN A THREEPHASE PIEZOELECTRIC COMPOSITE CONSTITUTIVE MODEL

An in-depth investigation is made on the problem of an arc-shaped interface insulating crack in a three-phase concentric circular cylindrical piezoelectric composite constitutive model. An exact solution in series form is derived by employing the complex variable method. In addition, the distribution of physical quantities such as stresses, strains, electric displacements and electric fields in the whole field and along the interface is also presented. Explicit expressions for crack opening displacement, jump in electric potential on the crack surface and the electro-elastic field intensity factors at the crack tips are obtained. Specific calculations demonstrate that the convergence of the series form solution is satisfactory and that the outer phase (composite phase) will exert a significant effect on the electro-mechanical coupling response of the composite system. Owing to the fact that stresses and electric displacements still possess conventional inverse square root singularities, the oscillating singularities near the crack tip under plane strain conditions will be absent and, as a result, no unphysical interpenetration phenomenon of the two crack surfaces will occur. In conclusion, the elastic solution obtained is also based on a solid physical foundation. Project supported by the National Natural Science Foundation of China (No.59635140), and the Doctorate Foundation of Xi'an Jiaotong University.     

On the Ising Model with Strongly Anisotropic External Field

In this paper we analyze the equilibrium phase diagram of the two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexistence lines disappear at every positive sufficiently small temperature, whereas one (and only one) of them persists for sufficiently low temperature.     

Quantum simulations of toroidal electric ring currents and magnetic fields in linear molecules induced by circularly polarized laser pulses

Circularly polarized laser pulses may excite state selective unidirectional toroidal electric ring currents around the axis of oriented linear molecules. These in turn induce state selective magnetic fields. Quantum simulations for AlCl show that these effects are about one or even more than three orders of magnitudes larger than those which may be prepared in oriented planar molecules such as Mg-porphyrin, by means of either circularly polarized laser pulses, or by traditional magnetic fields, respectively.     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.