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2002

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Articles 1 - 14 of 14

Full-Text Articles in Physics

Asymptotic Solitons For A Higher-Order Modified Korteweg–De Vries Equation, T. Marchant Oct 2002

Asymptotic Solitons For A Higher-Order Modified Korteweg–De Vries Equation, T. Marchant

Tim Marchant

Solitary wave interaction for a higher-order modified Korteweg–de Vries (mKdV) equation is examined. The higher-order mKdV equation can be asymptotically transformed to the mKdV equation, if the higher-order coefficients satisfy a certain algebraic relationship. The transformation is used to derive the higher-order two-soliton solution and it is shown that the interaction is asymptotically elastic. Moreover, the higher-order phase shifts are derived using the asymptotic theory. Numerical simulations of the interaction of two higher-order solitary waves are also performed. Two examples are considered, one satisfies the algebraic relationship derived from the asymptotic theory, and the other does not. For the example …

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Ultrafast Measurement Of Two-Photon Absorption By Loss Modulation, Peifang Tian, Warren Warren Aug 2002

Ultrafast Measurement Of Two-Photon Absorption By Loss Modulation, Peifang Tian, Warren Warren

Peifang Tian

We demonstrate a direct and sensitive technique for measuring two-photon absorption (TPA).An intensity- modulated femtosecond laser beam passes through a sample exhibiting TPA.A TPA signal at twice the modulation frequency is then generated and subsequently measured by a lock-in amplifier. The absolute TPA cross section of Rhodamine 6G at 800nm is found to be 15.32.010 -50 cm 4 s / photon and agrees well with previously published results obtained with much higher intensity [J.Chem.Phys. 112, 9201 (2000)]. Our method may be especially useful in measuring nonlinear absorptions of nonfluorescent materials.

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Infrared Depletion Spectroscopy Of Aniline-Acetonitrile Cation And Aniline-Acetonitrile-Water Cation Clusters, H. Nagai, Naveed Piracha, T. Nakanaga Aug 2002

Infrared Depletion Spectroscopy Of Aniline-Acetonitrile Cation And Aniline-Acetonitrile-Water Cation Clusters, H. Nagai, Naveed Piracha, T. Nakanaga

Naveed K. Piracha

The vibrational spectra of the aniline-acetonitrile^+ and the aniline-acetonitrile-water^+ cluster cations have been measured by the infrared depletion spectroscopy in the frequency region of NH and OH stretching vibrations. One absorption band was observed at 3437cm^-^1 in the infrared spectrum of the aniline-acetonitrile^+ cluster cation, and was assigned to the NH stretching vibration of free NH of aniline. As for the aniline-water-acetonitrile^+ cluster cation, three absorptions were observed at 3722, 3634 and 3247cm^-^1, which were assigned to the anti-symmetric stretching and symmetric stretching vibrations of OH of water and the stretching vibrations of NH bond interacting with water, respectively. In …

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Electrical Conductivity And Thermopower Of Cu–Sio[Sub 2] Nanogranular Films., W. Chen, J. Lin, X. Zhang, H. Shin, Jeffrey Dyck, C. Uher Jul 2002

Electrical Conductivity And Thermopower Of Cu–Sio[Sub 2] Nanogranular Films., W. Chen, J. Lin, X. Zhang, H. Shin, Jeffrey Dyck, C. Uher

Jeffrey Dyck

We have measured the thermopower S and electrical conductivity σ in a series of Cu[sub x](SiO[sub 2])[sub 1-x] nanogranular films between 2 and 300 K with Cu volume fraction x varying from 0.43 up to 1.0. At low temperatures, disorder-enhanced electron-electron interaction effects dictate the behavior of σ. A crossover of the temperature dependence from σ∝ √T to σ∝ T[sup 1/3] is observed as x is lowered and the metal-insulator transition is approached. S is small, shows linear temperature dependence, and is rather insensitive to the change of x. Effects of annealing are also discussed.

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Infrared Spectroscopy Of Aniline–Ne Clusters And The Corresponding Cluster Cations In The Nh2-Stretching Vibration Region, Naveed Piracha, T. Nakanaga Jun 2002

Infrared Spectroscopy Of Aniline–Ne Clusters And The Corresponding Cluster Cations In The Nh2-Stretching Vibration Region, Naveed Piracha, T. Nakanaga

Naveed K. Piracha

The vibrational spectra of the NH2-stretching modes of aniline–Ne and aniline–Ne+ have been measured using infrared depletion spectroscopy and REMPI–TOF mass spectrometry. In the NH2-stretching vibration region of the aniline–Ne clusters, two absorption bands at 3422 and 3508cm−1 were observed. The frequency shifts from the monomer was found to be negligibly small. As for the aniline–Ne+ cluster cations, the observed frequencies of the vibrational modes were 3394 and 3488cm−1. These values agreed with ones observed for aniline–Ar+ cluster within the error limit. This fact suggests that the effect of neon to aniline in forming the cluster is not significant in …

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Low-Temperature Ferromagnetism And Magnetic Anisotropy In The Novel Diluted Magnetic Semiconductor Sb2−Xvxte3, Jeffrey Dyck, Wei Chen, Pavel Hájek, Petr Lošt’Ák, Ctirad Uher Feb 2002

Low-Temperature Ferromagnetism And Magnetic Anisotropy In The Novel Diluted Magnetic Semiconductor Sb2−Xvxte3, Jeffrey Dyck, Wei Chen, Pavel Hájek, Petr Lošt’Ák, Ctirad Uher

Jeffrey Dyck

We report on a novel diluted magnetic semiconductor based on the Sb2Te3 tetradymite structure doped with very low concentrations of vanadium (1–3at%). Anisotropy in the magnetic hysteresis loops and magnetoresistance are observed at temperatures below the ferromagnetic ordering temperature. A Curie temperature of 24K is observed for Sb1.97V0.03Te3.

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High-Order Interaction Of Solitary Waves On Shallow Water, Prof. Tim Marchant Dec 2001

High-Order Interaction Of Solitary Waves On Shallow Water, Prof. Tim Marchant

Tim Marchant

The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg-de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both right- and left-moving waves, is derived to third order. A fourth-order interaction term, in which the right- and left-moving waves are coupled, is also derived as this term is crucial in determining the fourth-order change in solitary wave amplitude. The form of …

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The Occurrence Of Limit-Cycles During Feedback Control Of Microwave Heating, Prof. Tim Marchant Dec 2001

The Occurrence Of Limit-Cycles During Feedback Control Of Microwave Heating, Prof. Tim Marchant

Tim Marchant

The microwave heating of one- and two-dimensional slabs, subject to linear feedback control, is examined. A semianalytical model of the microwave heating is developed using the Galerkin method. A local stability analysis of the model indicates that Hopf bifurcations occur; the regions of parameter space in which limit-cycles exist are identified. An efficient numerical scheme for the solution of the governing equations, which consist of the forced heat equation and a Helmholtz equation describing the electric-field amplitude, is also developed. An excellent comparison between numerical solutions of the semianalytical model and the governing equations is obtained for the temporal evolution …

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Cubic Autocatalytic Reaction-Diffusion Equations: Semi-Analytical Solutions, Prof. Tim Marchant Dec 2001

Cubic Autocatalytic Reaction-Diffusion Equations: Semi-Analytical Solutions, Prof. Tim Marchant

Tim Marchant

The Gray-Scott model of cubic-autocatalysis with linear decay is coupled with diffusion and considered in a one-dimensional reactor (a reaction-diffusion cell). The boundaries of the reactor are permeable, so diffusion occurs from external reservoirs that contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations. The ordinary differential equations are then analysed to obtain semi-analytical results for the reaction-diffusion cell. Steady-state concentration profiles and bifurcation diagrams are obtained …

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Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant Dec 2001

Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant

Tim Marchant

A prototype chemical reaction is examined in both one and two-dimensional continuous-flow microwave reactors, which are unstirred so the effects of diffusion are important. The reaction rate obeys the Arrhenius law and the thermal absorptivity of the reactor contents is assumed to be both temperature- and concentration-dependent. The governing equations consist of coupled reaction-diffusion equations for the temperature and reactant concentration, plus a Helmholtz equation describing the electric-field amplitude in the reactor. The Galerkin method is used to develop a semi-analytical microwave reactor model, which consists of ordinary differential equations. A stability analysis is performed on the semi-analytical model. This …

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The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant Dec 2001

The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant

Tim Marchant

The initial boundary-value problem for the Korteweg-de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one boundary condition needed at x = 0 for the positive quarter-plane problem. Solutions of the KdV equation on the infinite line, such as the soliton, cnoidal wave, mean height variation and undular bore solution, are used to find approximate …

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The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant Dec 2001

The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant

Tim Marchant

The microwave heating of three-dimensional blocks, by the transverse magnetic waveguide mode TM11, is considered in a long rectangular waveguide. The governing equations are the forced heat equation and a steady-state version of Maxwell's equations, while the boundary conditions take into account both convective and radiative heat loss. Semi-analytical solutions, valid for small thermal absorptivity, are found using the Galerkin method. The electrical conductivity and the thermal absorptivity are assumed to be temperature dependent, while both the electrical permittivity and magnetic permeability are taken to be constant. Both a quadratic relation and an Arrhenius-type law are used for the temperature …

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Thermoelectric Properties Of K[Subscript 2]Bi[Subscript 8-X]Sb[Subscript X]Se[Subscript 13] Solid Solutions And Se Doping [Et Al.], Theodora Kyratski, Jeffrey Dyck, Wei Chen Dec 2001

Thermoelectric Properties Of K[Subscript 2]Bi[Subscript 8-X]Sb[Subscript X]Se[Subscript 13] Solid Solutions And Se Doping [Et Al.], Theodora Kyratski, Jeffrey Dyck, Wei Chen

Jeffrey Dyck

Our efforts to improve the thermoelectric properties of β-K2Bi8Se13, led to systematic studies of solid solutions of the type β-K2Bi8−xSbxSe13. The charge transport properties and thermal conductivities were studied for selected members of the series. Lattice thermal conductivity decreases due to the mass fluctuation generated in the lattice by the mixed occupation of Sb and Bi atoms. Se excess as a dopant was found to increase the figure-of merit of the solid solutions.

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Numerical Solitary Wave Interaction: The Order Of The Inelastic Effect, Prof. Tim Marchant Dec 2001

Numerical Solitary Wave Interaction: The Order Of The Inelastic Effect, Prof. Tim Marchant

Tim Marchant

Solitary wave interaction is examined using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects and is is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. The eBBM formulation is preferable to the eKdV equation for the numerical modelling of solitary wave collisions, due to the stability of its finite-difference scheme. In particular, it allows the interaction of steep waves to be modelled, which due to numerical instability, is not possible using the eKdV equation. Numerical simulations of a number of solitary wave collisions of varying nonlinearity are performed for two special cases corresponding to …

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