New results on systems with second-class constraints

We show how, for large classes of systems with purely second-class constraints, further information can be obtained about the constraint algebra. In particular, a subset consisting of half the full set of constraints is shown to have vanishing mutual brackets. Some other constraint brackets are also shown to be zero. The class of systems for which our results hold includes examples from non-relativistic particle mechanics as well as relativistic field theory. The results are derived at the classical level for Poisson brackets, but in the absence of commutator anomalies the same results will hold for the commutators of the constraint operators in the corresponding quantised theories.

Gauge-invariant reformulation of theories with second-class constraints

Given a classical dynamical theory with second-class constraints, it is sometimes possible to construct another theory with first-class constraints, i.e., a gauge-invariant one, which is physically equivalent to the first theory. We identify some conditions under which this may be done, explaining the general principles and working out several examples. Field theoretic applications include the chiral Schwinger model and the non-linear sigma model. An interesting connection with the work of Faddeev and Shatashvili is pointed out.

Crumpling and second sound in lyotropic lamellar phases

We study relative concentration fluctuations in two component lamellar smectic liquid crystals consisting of surfactant layers of width w separated by a background fluid and show that these fluctuations are dominated by crumpling fluctuations of the surfactant layers when (w/l)2

Second harmonic generation in poled molecularly doped polymer films : Push-pull butadienes in poly(methyl methacrylate) and polystyrene

We report second harmonic generation in a new class of organic materials, namely donor-acceptor substituted all-trans butadienes doped in poly(methyl methacrylate) or polystyrene and oriented by corona poling at elevated temperatures. Second harmonic measurements were made at room temperature. The observed d33 coefficients are greater than those of potassium dihydrogen phosphate or 4-dimethylamino-4'-nitrostilbene doped in similar polymer matrices. Rotational diffusion coefficients estimated from the decay characteristics of the second harmonic intensity in the polymer films indicate that the polymer matrix plays a major role in stabilizing the dopants in a nonlinear optics conducive environment.

Molecular Dynamics Simulations of Orientational Relaxation in Dipolar Lattice: Lack of Diffusive Decay for Second and Higher Rank Correlation Functions

Extensive molecular dynamics simulations have been carried out to calculate the orientational correlation functions Cl(t), G(t) = [4n/(21 + l)]Ci=-l (Y*lm(sZ(0)) Ylm(Q(t))) (where Y,,(Q) are the spherical harmonics) of point dipoles in a cubic lattice. The decay of Cl(t) is found to be strikingly different from higher l-correlation functions-the latter do not exhibit diffusive dynamics even in the long time. Both the cumulant expansion expression of Lynden-Bell and the conventional memory function equation provide very good description of the Cl(t) in the short time but fail to reproduce the observed slow, long time decay of c1 (t) .

Influence of poling methods on the orientational dynamics of 2-methyl-4-nitro-aniline in poly(methyl methacrylate) studied by second harmonic generation

The magnitude and stability of the induced dipolar orientation of 2-methyl-4-nitroaniline (MNA)/poly(methyl methacrylate) (PMMA) guest/host system is investigated. The chromophores are aligned using both the corona discharge and contact electrode poling techniques. The magnitude of order parameter (also an indicator for the second order nonlinear susceptibility) is measured by recording absorbances of the poled (by the two different techniques) and unpoled PMMA films at different concentrations of MNA. Under the same conditions the corona poling technique creates a higher alignment of molecules along the field direction. The time dependence of the second harmonic intensity of the MNA/PMMA film prepared by the two techniques can be described by a Kohlrausch-Williams-Watts stretched exponential. The temperature dependence of the decay time constant is found to generally follow a modified Williams-Landel-Ferry (WLF) or Vogel-Tamann-Fulcher (VTF) equation. The glass transition temperature seems to be the single most important parameter for determining the relaxation time tau(T).

On boundedness and parallel to center dot parallel to(p) continuity of second quantisation

in this short note, we determine precisely which operators have the property that their (full, symmetric or antisymmetric) second quantisation is an operator which is bounded or belongs to one of the various Schatten ideals; we also note that in 'the interior' of the natural domain, the second quantisation is a continuous map.

Highly Efficient and Thermally Stable Second-Order Nonlinear Optical Chromophores and Electrooptic Polymers

Organic polymeric electro-optic (E-O) materials have attracted significant attention because of their potential use as fast and efficient components of integrated photonic devices (1,2). However, the practical application of these materials in optical devices is somewhat limited by the stringent material requirements imposed by the device design, fabrication processes and operating environments. Among the various material requirements, the most notable ones are large electro-optic coefficients (r(33)) and high thermal stability (3). The design of poled polymeric materials with high electro-optic activity (r(33)) involves the optimization of the percent incorporation of efficient (large beta mu) second order nonlinear optical (NLO) chromophores into the polymer matrices and the effective creation of poling-induced non-centrosymmetric structures. The factors that affect the material stability are a) the inherent thermal stability of the NLO chromophores, b) the chemical stability of the NLO chromophores during the polymer processing conditions, and c) the long-term dipolar alignment stability at high temperatures. Although considerable progress has been made in achieving these properties (4), organic polymeric materials suitable for practical E-O device applications are yet to be developed. This chapter highlights some of our approaches in the optimization of molecular and material nonlinear optical and thermal properties.

Solution of a hypersingular integral equation of the second kind

A straightforward analysis involving the complex function-theoretic method is employed to determine the closed-form solution of a special hypersingular integral equation of the second kind, and its known solution is recovered.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.

Aryl monosulphides and symmetrical disulphides based second order nonlinear optical chromophores with transparency in the visible

A series of aryl monosulphides and disulphides have been synthesized and characterized. Their molecular hyperpolarizability (beta) has been measured in solution with the hyper-Rayleigh Scattering technique and also calculated by semiempirical AMI method. The trend in the observed and calculated values of first hyperpolarizability of these compounds has been found to be in good agreement. These compounds show moderate P values and excellent transparency in the visible region.

Synthesis and characterization of mono- and bis-D-pi-A cryptand derivatives for second-order nonlinear optics and its modulation with different metal ion inputs

Two new classes of mono- and bis-D-pi-A cryptand derivatives with a flexible and a rigid cryptand core have been synthesized. The linear and nonlinear optical properties of these molecules are probed. The three dimensional cavity of the cryptand moiety has been utilized to modulate the SHG intensity to different extents in solution with metal ion inputs such as Ni-II,Cu-II,Zn-II, and Cd-II. We also report that decomplexation events can be used to reversibly modulate their NLO responses.

Unsymmetrical aryl disulfides with excellent transparency in the visible region for second order nonlinear optics

Several unsymmetrically substituted aromatic donor acceptor disulfides have been synthesized and analysed for their second order nonlinear optical properties. These molecules exhibit moderately high first hyperpolarizability (beta) with excellent transparency in the visible region. Most of the unsymmetrical disulfides have a cut-off wavelength below 420 nm. Calculations show that the molecules have an asymmetric charge distribution around the disulfide bond which is responsible for their high beta values. These results provide motivation for the design and synthesis of nonlinear optical chromophores with multiple disulfide bonds for large second order nonlinearity and excellent visible transparency.

Effect of spinel second phase on high temperature deformation in alumina

Constant stress compression creep experiments were carried out on high purity alumina composites with spinel contents of 8 and 30%, corresponding to a situation with isolated and interconnected second phases. The creep experiments were conducted over a stress and temperature range of 10 to 150 MPa and 1623 to 1723 K, respectively. Analysis of the experimental data indicated that the variation in spinel content did not have any influence on high temperature deformation in the composite. The spinel phase retards grain growth, and this may enhance superplasticity in alumina-spinel composites.