Braid theory and Zipf-Mandelbrot relation used in microparticle dynamics

A study is presented of the dynamics of a few body system of microparticles by using rank-ordering statistics in order to gain insight in the magneto-rheological properties of ferrofluids. This dynamical system is made up of micrometer sized plastic spheres dispersed in a ferrofluid driven by external magnetic fields. The world lines of the microspheres are captured and the dynamical modes are described by mathematical braid theory. Rank-ordering statistics on these modes shows a wide power law region consistent with the Zipf-Mandelbrot relation. We have also performed numerical simulations of the experimental system which show results in agreement with the observations.     

Helicon-phonon interaction for oblique propagation in potassium

The dispersion equation for oblique propagation of the wave in thexy plane for helicon-phonon interaction has been derived and numerical studies have been carried out on the nature of variation of the four different modes with the magnetic field and the inclination of the magnetic field with the direction of propagation.     

Asymptotic analysis of wall modes in a flexible tube revisited

The stability of wall modes in fluid flow through a flexible tube of radius R surrounded by a viscoelastic material in the region R < r < HR is analysed using a combination of asymptotic and numerical methods. The fluid is Newtonian, while the flexible wall is modelled as an incompressible viscoelastic solid. In the limit of high Reynolds number (Re), the vorticity of the wall modes is confined to a region of thickness O(Re ^-1/3) in the fluid near the wall of the tube. Previous numerical studies on the stability of Hagen-Poiseuille flow in a flexible tube to axisymmetric disturbances have shown that the flow could be unstable in the limit of high Re, while previous high Reynolds number asymptotic analyses have revealed only stable modes. To resolve this discrepancy, the present work re-examines the asymptotic analysis of wall modes in a flexible tube using a new set of scaling assumptions. It is shown that wall modes in Hagen-Poiseuille flow in a flexible tube are indeed unstable in the limit of high Re in the scaling regime Re∼Σ^3/4. Here Σ is a nondimensional parameter characterising the elasticity of the wall, and Σ≡ρGR ²/η², where ρ and η are the density and viscosity of the fluid, and G is the shear modulus of the wall medium. The results from the present asymptotic analysis are in excellent agreement with the previous numerical results. Importantly, the present work shows that the different types of unstable modes at high Reynolds number reported in previous numerical studies are qualitatively the same: they all belong to the class of unstable wall modes predicted in this paper. Received 12 June 2000 and Received in final form 8 November 2000     

Angular tuning of defect modes spectrum in the one-dimensional photonic crystal with liquid-crystal layer

A one-dimensional ZrO₂/SiO₂ photonic crystal with a 4-n -pentyl-4' -cyanobiphenyl (5CB) nematic defect layer was used to investigate the transmission spectra of light polarized parallel and perpendicular to the liquid-crystal director at different angles of incidence. The spectra of the photonic crystal were shown to split into four polarized components T_ij at oblique incidence. When the incident angle increased, the bandgap edges and the defect modes shifted towards short wavelengths, while the amplitudes of the defect modes increased for the transverse magnetic polarization and decreased for the transverse electric polarization. The observed discrepancy between the defect mode amplitudes in the center and near the edges of the photonic bandgap was found to be related to the radiation losses inside the defect layer of a non-ideal photonic crystal. The simulated transmission spectra obtained using recurrence relations and taking into account the decay of defect modes are in good agreement with the experimental data.     

Collision of a 1-D column of beads with a wall

An experimental study of the collision of a column of N beads () with a fixed wall is presented. For a fixed height of fall and a rigid wall, we show that the maximum force felt by the wall is independent of the number of beads N. The duration of impact, the velocity of the deformation wave in the column and an effective restitution coefficient of the column are also measured as a function of N. For a soft wall, we show that the maximum force depends on N. A non-dissipative numerical model, based on a nonlinear interaction law between nearest neighbours, gives results in agreement with the experimental data. Moreover, we show that, after the compression phase, the beads of the top of the column separate one after the other from the column with a velocity greater than the initial one. The beads at the bottom then bounce upwards in block, with a velocity smaller than the initial one. We emphasize that this detachment effect results from the energy redistribution within the whole system during the collision and not from any dissipative effect. Received: 6 February 1998 / Revised and accepted: 26 May 1998     

Pattern dynamics in an annular laser

Competition among modes in an annular CO₂ laser has been experimentally and numerically analyzed. During the coexistence of different patterns, each of them resulting from the interaction of two transverse modes with opposite angular momentum, chaos has been experimentally detected. A numerical model, derived from the Maxwell-Bloch equations and including symmetry breaking terms, enables the interpretation of the main experimental features. Received 10 March 2000     

Simulations of inelastic electron tunneling spectroscopy of semifluorinated hexadecanethiol junctions

The inelastic electron tunneling spectroscopy (IETS) of semifluorinated hexadecanethiol junctions is theoretically studied. The numerical results show that the C-F vibration modes of semifluorinated alkanethiol series can not be detected, and the C-H stretching mode in IETS is related to the CH₂ vibration. It is demonstrated that the Raman modes are preferred over IR modes in IETS, which is in good agreement with the experimental measurements presented by Beebe et al. [Nano Lett., 2007, 7(5): 1364].      

Modal Birefringence Dependent Supercontinuum Due to Cross-Phase Modulation in a Dispersion-Flattened/Decreasing Fiber

It was found by numerical analysis that a 320 nm wide and flat spectrum at 20 dB less than the central maximum intensity is generated from cross-phase modulated soliton pulses with 3.5 ps pulse width and 2.3 W peak power, which are propagated through a 2.4km length of dispersion-flattened/decreasing fiber (DFDF). The cross-phase modulation (XPM) at a central wavelength of 1.55 μm is achieved by exciting two orthogonally polarized modes into the principal axes. The wave-vector mismatch between the orthogonal pulses can be neglected because of soliton trapping when the modal birefringence of the DFDF is less than |n_ox - n_0y| = 10⁻⁶. The effect of modal birefringence on supercontinuum generation is discussed in temporal and spectral regimes by numerical analysis.     

Cyclotron resonance of polarons in ternary mixed crystals

Rayleigh-Schr?dinger perturbation theory and an improved Wigner-Brillouin perturbation theory has been used to study the cyclotron resonance of the polarons in ternary mixed crystals in the zero-temperature limit. The interaction between an electron and two branches of longitudinal optical phonon modes is taken into account in the framework of the random-element-isodisplacement model. The numerical results for several ternary mixed crystals show that the polaronic cyclotron energy and mass split successively twice related to the higher and lower branches of longitudinal optical phonon modes of ternary mixed crystals. A non-linear dependence of the polaronic cyclotron energy and mass on the composition x is found. Received 19 March 2002 / Received in final form 21 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: xxliang@imu.edu.cn     

Coherent backscattering and localization in a self-attracting random walk model

Intensity propagation of waves in dilute 2D and 3D disordered systems is well described by a random walk path-model. In strongly scattering media, however, this model is not quite correct because of interference effects like coherent backscattering. In this letter, coherent backscattering is taken into account by a modified, self-attracting random walk. Straightforward simulations of this model essentially reproduce the results of current theories on “non-classical” transport behavior, i.e. Anderson localization in 1D and 2D for any amount of disorder and a phase transition from weak to strong localization in 3D. However, in the strongly scattering regime corrections are necessary to account for the finite number of light modes due to their non-vanishing lateral extention. Within our model this correction leads to the observation that strong localization does not take place. Received 17 September 2001     

Analysis and Calculations of Forbidden Regions for Transverse-Electric-Guided Waves in the Three-Layer Planar Waveguide with Photonic Metamaterial

Abstract

In this article, the modal theory was used to analyze transverse electric waves in the three-layer planar waveguide with photonic metamaterial. The formulas for the electric fields of transverse electric modes in this structure have been proposed. There always exist two forbidden regions for transverse electric waves in the three-layer planar waveguide with photonic metamaterial. The complete set of modes of all possible solutions for the transverse electric waves in the three-layer planar waveguide with photonic metamaterial had been analyzed and discussed. Similar processes can be extensively used to predict the propagation characteristics of TM waves in the three-layer planar waveguide with photonic metamaterial. The analytical and numerical results show excellent agreement.     

Cooperative frequency locking and tristability in a class-B laser

The locking and unlocking phenomena of the modes of the transverse familyq=1 in a CO₂ laser are investigated. The experimental results show three characteristic regions: a bistability between two helical waves of opposite handedness, a tristability among the two helicities of opposite handedness and an unlocked state, and the unlocked state. Near the locking threshold, oscillations which can be interpreted as due to the oscillations of the modal amplitudes and relative phase are also observed. These results are found to be consistent with solutions of the two-mode Maxwell-Bloch equations for class-B lasers.     

Electron phonon interactions and superconductivity in α ′ -TTF[Pd(dmit)2]2

A simple model is developed to understand superconductivity in α ^′ -TTF[Pd(dmit)₂]₂. We include electron-intra molecular and intermolecular phonon interactions as the mechanism of superconductivity. Intramolecular vibrations included are the eight symmetric A_g modes of the Pd(dmit)₂ molecule. Intermolecular vibrations included are the longitudinal acoustic and transverse acoustic (LA and TA) modes of the Pd(dmit)₂ column. All the electron-phonon coupling constants are calculated from first principles. We find that largest el-intramolecular vibration coupling is to the A_g mode with the highest frequency (1449 cm^-1). The el-intermolecular coupling to the LA mode is found to be larger than the total el-intramolecular couplings. We also find el-(TA)phonon coupling to be at least an order of magnitude smaller than el-(LA)phonon coupling. Estimate of superconducting transition temperature is comparable to experimental result. We also provide a detailed discussion, employing the results of recent numerical calculations on two-chain Hubbard model and the specific material parameters, on the relative importance of el-ph and Coulomb-origin mechanisms of superconductivity in α ^′ -TTF[Pd(dmit)₂]₂ and TTF[Ni(dmit) ₂ ] ₂ . Received 29 March 2001 and Received in final form 7 August 2001     

Visualizing color plasma instabilities

I discuss recent advances in the understanding of non-equilibrium gauge field dynamics in plasmas which have particle distributions which are locally anisotropic in momentum space. In contrast to locally isotropic plasmas such anisotropic plasmas have a spectrum of soft unstable modes which are characterized by exponential growth of transverse (chromo)-magnetic fields at short times. The long-time behavior of such instabilities depends on whether or not the gauge group is Abelian or non-Abelian. I will report on recent numerical simulations which attempt to determine the long-time behavior of an anisotropic non-Abelian plasma within hard-loop effective theory. For novelty I will present an interesting method for visualizing the time dependence of SU(2) gauge field configurations produced during our numerical simulations.     

Quantum corrections to the conductance of a square quantum dot with soft confinement

We study the conductance of a square quantum dot, modeling the potential with a self-consistent Thomas-Fermi approximation. The resulting potential is characterized by level statistics indicative of mixed chaotic and regular electron dynamics within the dot in spite of the regular geometry of the gates defining the dot. We calculate numerically, for the case of a quantum dot with soft confinement, the weak localization (WL) correction. We demonstrate that this confining potential may generate either Lorentzian or linear lineshapes depending on the number of modes in the leads. Finally, we present experimental WL data for a lithographically square dot and compare the results with numerical calculations. We analyze the experimental results and numerical simulations in terms of semiclassical and random matrix theory (RMT) predictions and discuss their limitations as far as real experimental structures are concerned. Our results indicate that direct application of the above predictions to distinguish between chaotic and regular dynamics in a particular cavity can not always lead to reliable conclusions as the shape and magnitude of the WL correction can be strongly sensitive to the geometry-specific, non-universal features of the system. Received 13 May 1998     

Electromagnetic-wave propagation in one boundary-corrugated parallel-plate wave guide filled with uniaxial warm drifting plasma

Summary The e.m. wave propagation in a parallel-plate wave guide withone boundary corrugated and filled with uniaxial warmdrifting plasma has been studied. The dispersion relation and the field expressions for the TM-modes have been derived. The effects of the temperature and the drift velocity on the propagation modes have been studied in detail. The fast and the slow waves are greatly affected by the temperature and the drift velocity, whereas the wave guide wave is insignificantly affected. The effect of the corrugation has also been discussed. The dispersion relation of the TE-modes, in this case, has been derived and found to be same as that of the wave guide filled with free space. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Single-mode condition for silicon rib waveguides with trapezoidal cross-section

Single-mode condition for silicon rib waveguides with trapezoidal cross-section was obtained using a numerical method based on imaginary-distance beam propagation method with non-uniform discretization. Both quasi-transverse-electric and quasi-transverse-magnetic modes were investigated. Simulated single-mode condition is given by a modified equation. Comparison with reported results shows that the Marcatili’s method is in a better agreement with our results.