Spontaneous emission from radiative chiral nematic liquid crystals at the photonic band-gap edge: an investigation into the role of the density of photon states near resonance.

In this article, we investigate the spontaneous emission properties of radiating molecules embedded in a chiral nematic liquid crystal, under the assumption that the electronic transition frequency is close to the photonic edge mode of the structure, i.e., at resonance. We take into account the transition broadening and the decay of electromagnetic field modes supported by the so-called "mirrorless"cavity. We employ the Jaynes-Cummings Hamiltonian to describe the electron interaction with the electromagnetic field, focusing on the mode with the diffracting polarization in the chiral nematic layer. As known in these structures, the density of photon states, calculated via the Wigner method, has distinct peaks on either side of the photonic band gap, which manifests itself as a considerable modification of the emission spectrum. We demonstrate that, near resonance, there are notable differences between the behavior of the density of states and the spontaneous emission profile of these structures. In addition, we examine in some detail the case of the logarithmic peak exhibited in the density of states in two-dimensional photonic structures and obtain analytic relations for the Lamb shift and the broadening of the atomic transition in the emission spectrum. The dynamical behavior of the atom-field system is described by a system of two first-order differential equations, solved using the Green's-function method and the Fourier transform. The emission spectra are then calculated and compared with experimental data.

Finite horizon LQR control with limited controller-system communication

We consider finite-horizon LQR control with limited controller-system communication. Within a time-horizon T , the controller can only communicate with the system dfirst-order systems and a class of higher-order systems. We also discuss when such a control data schedule remains optimal (or is near optimal) for general systems. © 1963-2012 IEEE.

First-Principles Study of Magnetic Properties of 3d Transition Metals Doped in ZnO Nanowires

The defect formation energies of transition metals (Cr, Fe, and Ni) doped in the pseudo-H passivated ZnO nanowires and bulk are systematically investigated using first-principles methods. The general chemical trends of the nanowires are similar to those of the bulk. We also show that the formation energy increases as the diameter of the nanowire decreases, indicating that the doping of magnetic ions in the ZnO nanowire becomes more difficult with decreasing diameter. We also systematically calculate the ferromagnetic properties of transition metals doped in the ZnO nanowire and bulk, and find that Cr ions of the nanowire favor ferromagnetic state, which is consistent with the experimental results. We also find that the ferromagnetic coupling state of Cr is more stable in the nanowire than in the bulk, which may lead to a higher T (c) useful for the nano-materials design of spintronics.

Mode coupling between first- and second-order whispering-gallery modes in coupled microdisks

The mode characteristics for two coupled microdisks are investigated by the finite-difference time-domain technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first- and second-order WGMs can have a crossing point in some cases, which can induce anticrossing mode coupling between them and greatly reduce the mode Q factor of the coupled first-order WGMs. The time variation of mode field pattern shows the transformation between the coupled first- and second-order WGMs. (C) 2007 Optical Society of America

First and second order Raman scattering spectroscopy of nonpolar a-plane GaN

Nonpolar a-plane [(1120)] GaN samples have been grown on r-plane [(1102)] sapphire substrates by low-pressure metal-organic chemical-vapor deposition. The room-temperature first and second order Raman scattering spectra of nonpolar a-plane GaN have been measured in surface and edge backscattering geometries. All of the phonon modes that the selection rules allow have been observed in the first order Raman spectra. The frequencies and linewidths of the active modes have been analyzed. The second order phonon modes are composed of acoustic overtones, acoustic-optical and optical-optical combination bands, and optical overtones. The corresponding assignments of second order phonon modes have been made. (c) 2007 American Institute of Physics.

Multipolar model for collisional quantum interference on rotational energy transfer

A theoretical model of collisional quantum interference (CQI) is developed in a diatom-diatom system based on the first-order Born approximation of time-dependent perturbation theory and the multipolar interaction potential. The transition cross section is obtained. The relations between the differential and integral interference angles are discussed. The key factors on the determination of the differential and integral interference angles are obtained. The changing tendency of the interference angles with the experimental temperatures is obtained.

APPLICATION OF ULTRAMICROELECTRODES IN STUDIES OF HOMOGENEOUS CATALYTIC REACTIONS .3. THE CONDITION FOR QUASI-1ST AND 2ND-ORDER HOMOGENEOUS CATALYTIC REACTIONS AT ULTRAMICRODISK ELECTRODES IN THE STEADY-STATE

The conditions for quasi-first and second order homogeneous catalytic reactions and their variation with each other at an ultramicrodisk electrode in the steady state are discussed in this paper. The order of reaction can be controlled by changing the dimension of the ultramicroelectrode: the second order reaction can be changed to quasi-first by decreasing the dimension of the ultramicroelectrode. An example of this is given. The main factor effect on the reaction order is the dimension of the ultramicroelectrode. The K4Fe(CN)6-aminopyrine system is selected to confirm the theory, the experiments showing that the system is a second order reaction at a 432 mum microelectrode, and a quasi-first order reaction at a 19 mum ultramicroelectrode. The kinetic constant of the system can be determined by applying the previous theory of homogeneous catalytic reaction.

THE CATALYTIC BEHAVIOR AND REACTION-MECHANISM OF THE BI-CE-O SYSTEM CATALYSTS IN THE OXIDATIVE DEHYDROAROMATIZATION OF PROPYLENE

Oxidative dehydroaromatization of propylene was investigated by the pulse technique over two kinds of single oxide catalysts. With the Bi2O3 catalyst, the main dimer product was 1,5-hexadiene, and the dimerization activity was stable to pulse number even if the catalyst was partly reduced to the bulk. With the CeO2 catalyst, benzene was mainly formed instead of 1,5-hexadiene, but the activity decreased rapidly with increasing pulse number, indicating that only the lattice oxygen near the catalyst surface could be used for oxidative dimerization and the further aromatization. The Bi-Ce-O system catalyst was found in this study to give higher aromatization activity and showed better stability, compared to the Bi-Sn-O catalyst. Although the Bi-Ce-O catalyst was only a mixture of the two component oxides from X-ray diffraction analysis, there was a significant combination effect on the selectivity to benzene. The highest and the most stable selectivity of benzene was obtained at Bi/Ce = 1. In the TPD spectrum of Bi-Ce-O catalyst, there are not only the lattice oxygen (beta-oxygen) over 620-degrees-C due to the reduction of Bi2O3, but also a great deal of the alpha-oxygen desorbed about 400-degrees-C, which is considered the absorbed oxygen in the bulk. This absorbed oxygen could probably be a compensation of the lattice oxygen through the route of gaseous --> absorbed --> lattice oxygen in the binary catalyst system. By the kinetic study on the Bi-Ce-O catalyst, the dimer formation rate was the first-order with respect to the partial pressure of propylene and zero-order of oxygen. Although detail investigation would be made further, it was considered that the complete oxidation of propylene would mainly take place parallelly on some different sites, and the rate-determining step of propylene dimerization occurred probably between an adosrbed propylene and a gaseous one by an Eley-Rideal type mechanism.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Intrinsic dielectric response in ferroelectric nano-capacitors

Measurements on 'free-standing' single-crystal barium titanate capacitors with thickness down to 75 nm show a dielectric response typical of large single crystals, rather than conventional thin films. There is a notable absence of any broadening or temperature shift of the dielectric peak or loss tangent. Peak dielectric constants of similar to25 000 are observed, and Curie-Weiss analysis demonstrates first order transformation behaviour. This is in dramatic contrast to results on conventionally deposited thin film capacitor heterostructures, which show large dielectric peak broadening and temperature shifts (e.g. Parker et al 2002 Appl. Phys. Lett. 81 340), as well as an apparent change in the nature-of the paraelectric-ferroelectric transition from first to second order. Our data are compatible with a recent model by Bratkovsky and Levanyuk (2004 Preprint cond-mat/0402100), which attributes dielectric peak broadening to gradient terms that will exist in any thin film capacitor heterostructure. The observed recovery of first order transformation behaviour is consistent with the absence of significant substrate clamping in our experiment, as modelled by Pertsev et al (1998,Phys. Rev. Lett. 80 1988), and illustrates that the second order behaviour seen in conventionally deposited thin films cannot be attributed to the effects of reduced dimensionality in the system, nor to the influence of an intrinsic universal interfacial capacitance associated with the electrode- ferroelectric interface.

Dilute acid hydrolysis of cellulose and cellulosic bio-waste using a microwave reactor system

The dilute acid hydrolysis of grass and cellulose with phosphoric acid was undertaken in a microwave reactor system. The experimental data and reaction kinetic analysis indicate that this is a potential process for cellulose and hemi-cellulose hydrolysis, due to a rapid hydrolysis reaction at moderate temperatures. The optimum conditions for grass hydrolysis were found to be 2.5% phosphoric acid at a temperature of 175 degrees C. It was found that sugar degradation occurred at acid concentrations greater than 2.5% (v/v) and temperatures greater than 175 degrees C. In a further series of experiments, the kinetics of dilute acid hydrolysis of cellulose was investigated varying phosphoric acid concentration and reaction temperatures. The experimental data indicate that the use of microwave technology can successfully facilitate dilute acid hydrolysis of cellulose allowing high yields of glucose in short reaction times. The optimum conditions gave a yield of 90% glucose. A pseudo-homogeneous consecutive first order reaction was assumed and the reaction rate constants were calculated as: k(1) = 0.0813 s(-1); k(2) = 0.0075 s(-1), which compare favourably with reaction rate constants found in conventional non-microwave reaction systems. The kinetic analysis would indicate that the primary advantages of employing microwave heating were to: achieve a high rate constant at moderate temperatures: and to prevent 'hot spot' formation within the reactor, which would have cause localised degradation of glucose.

[Ag(NH3)(2)]ClO4: Crystal structures, phase transition, and vibrational spectra

[Ag(NH3)(2)](ClO4) is obtained from a solution of AgClO4 in cone. ammonia as colourless single crystals (orthorhombic, Pnmn, Z = 4, a = 795.2(1) pm, b 617.7(1) pm, c = 1298.2(2) pm, R-all = 0.0494). The structure consists of linearly coordinated cations, [Ag(NH3)(2)](+), stacked in a staggered conformation and of tetrahedral (ClO4)(-) anions. A first order phase transition was observed between 210 and 200 K and the crystal structure of the low-temperature modification (monoclinic. P2/m, Z = 4, a = 789.9(5) pm, b = 604.1(5) pm, c = 1290.4(5) pm, beta = 97.436(5)degrees, at 170 K, R-all = 0.0636) has also been solved. Spectroscopic investigations (IR/Raman) have been carried out and the assignment of the spectra is discussed.

Enhancement Factor for Gas Absorption in a Finite Liquid Layer. Part 2: First- and Second-Order Reactions in a Liquid in Plug Flow

Gas absorption accompanied by an irreversible chemical reaction of first-order or second-order in a liquid layer of finite thickness in plug flow has been investigated. The analytical solution to the enhancement factor has been derived for the case of a first-order reaction, and the exact solution to the enhancement factor has been obtained via numerical simulation for the case of a second-order reaction. The enhancement factor in both cases is presented as a function of the Fourier number and tends to deviate from the prediction of the existing enhancement factor expressions based on the penetration theory at Fourier numbers above 0.1 due to the absence of a well-mixed bulk region in the liquid layer. Approximate enhancement factor expressions that describe the analytical and exact solutions with an accuracy of 5?% and 9?%, respectively, have been proposed.