Energy level statistics for models of coupled single-mode Bose-Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.

Stability analysis based on birfurcation theory of the DSTATCOM operating in current control mode

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies.

Dynamics of mode transitions in inductively-coupled plasmas

The dynamics of transitions between the electrostatic and electromagnetic discharge modes of the low-frequency (460 kHz) inductively coupled plasma (LF ICP) reactor is studied. A series of images of plasma glows in Ar and N2 gases taken in the process of continuous variation of the input power confirms the discharge bistability and hysteresis. The operation regimes and parameters making the LF ICP reactor attractive for materials synthesis and processing applications are discussed.

Power transfer and mode transitions in low-frequency inductively coupled plasmas

Operation and mode jumps in low-frequency (500 kHz) radio-frequency inductively coupled plasmas are investigated. The discharge is driven by a flat inductive coil which can excite the electrostatic (E) and electromagnetic (H) discharge modes. The power transfer efficiency and mode transition behavior are studied. It is found that the power reflection coefficient as a function of the input power is minimal in the vicinity of the mode transitions and exhibits hysteresis, which is also observed when the operating gas pressure is varied.

Discharge mode transitions in low-frequency inductively coupled plasmas with internal oscillating current sheets

Transitions between the two discharge modes in a low-frequency (∼460 kHz) inductively coupled plasma sustained by an internal oscillating radio frequency (rf) current sheet are studied. The unidirectional rf current sheet is generated by an internal antenna comprising two orthogonal sets of synphased rf currents driven in alternately reconnected copper litz wires. It is shown that in the low-to-intermediate pressure range the plasma source can be operated in the electrostatic (E) and electromagnetic (H) discharge modes. The brightness of the E -mode argon plasma glow is found remarkably higher than in inductively coupled plasmas with external flat spiral "pancake" coils. The cyclic variations of the input rf power result in pronounced hysteretic variations of the optical emission intensity and main circuit parameters of the plasma source. Under certain conditions, it appears possible to achieve a spontaneous E→H transition ("self-transition"). The observed phenomenon can be attributed to the thermal drift of the plasma parameters due to the overheating of the working gas. The discharge destabilizing factors due to the gas heating and step-wise ionization are also discussed. © 2005 American Vacuum Society.

Optical emission characteristics and mode transitions in low-frequency inductively coupled plasmas

An attempt was made to investigate the optical emission spectra of atomic, molecular, and ionic species in low-frequency, high-density ICP discharges in pure nitrogen, ar con gases, and gas mixtures Ar+H2, N2+Ar, and N2+H2. The excited species were identified by in situ optical emission intensity (OEI) measurements in the discharge chamber. In general, significant results were obtained.

Hysteresis and mode transitions in a low-frequency inductively coupled plasma

The performance of the 500 KHz planar-coil inductively coupled plasma source was studied. The global electrical characteristics of the discharge, distributions of the induced electromagnetic fields, plasma density, potential, and electron temperature were investigated. Achieved high plasma density and low electron temperature implied that the studied plasma source was promising for industrial applications.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The axisymmetric mode

The coupled wavenumbers of a fluid-filled flexible cylindrical shell vibrating in the axisymmetric mode are studied. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter e due to the coupling. Using the smallness of Poisson's ratio (v), a double-asymptotic expansion involving e and v 2 is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (for large and small values of E). Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. The wavenumber solutions are continuously tracked as e varies from small to large values. A general trend observed is that a given wavenumber branch transits from a rigidwalled solution to a pressure-release solution with increasing E. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. Only the axisymmetric mode is considered. However, the method can be extended to the higher order modes.

Theory of combined AM and high-harmonic FM mode locked laser

Closed form solutions for a simultaneously AM and high-harmonic FM mode locked laser system is presented. Analytical expressions for the pulsewidth and pulsewidth-bandwidth products are derived in terms of the system parameters. The analysis predicts production of 17 ps duration pulses in a Nd:YAG laser mode locked with AM and FM modulators driven at 80 MHz and 1.76 GHz for 1 W modulator input power. The predicted values of the pulsewidth-bandwidth product lie between the values corresponding to the pure AM and FM mode locking values.

Axial wave propagation in coupled nanorod system with nonlocal small scale effects

This article deals with the axial wave propagation properties of a coupled nanorod system with consideration of small scale effects. The nonlocal elasticity theory has been incorporated into classical rod/bar model to capture unique features of the coupled nanorods under the umbrella of continuum mechanics theory. Nonlocal rod model is developed for coupled nanorods. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behavior of nanorods from those of macroscopic rods. Explicit expressions are derived for wavenumber, cut-off frequency and escape frequency of nanorods. The analysis shows that the wave characteristics of nanorods are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in axial or longitudinal wave mode, where no wave propagation occurs. This is manifested in the spectrum cures as the region, where the wavenumber tends to infinite or wave speed tends to zero. The effect of the coupled spring stiffness is also capture in the present analysis. It has been also shown that the cut-off frequency increases as the stiffness of the coupled spring increases and also the coupled spring stiffness has no effect on escape frequency of the axial wave mode in the nanorod. This cut-off frequency is also independent of the nonlocal small scale parameter. The present study may bring in helpful insights while investigating multiple-nanorod-system-models for future nano-optomechanical systems applications. The results can also provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of coupled single-walled carbon nanotubes or coupled nanorods. (C) 2011 Elsevier Ltd. All rights reserved.

Coupled phonons, magnetic excitations, and ferroelectricity in AlFeO3: Raman and first-principles studies

We determine the nature of coupled phonons and magnetic excitations in AlFeO3 using inelastic light scattering from 5 to 315 K covering a spectral range from 100 to 2200 cm(-1) and complementary first-principles density functional theory-based calculations. A strong spin-phonon coupling and magnetic ordering-induced phonon renormalization are evident in (1) anomalous temperature dependence of many modes with frequencies below 850 cm(-1), particularly near the magnetic transition temperature T-c approximate to 250 K, and (2) distinct changes in band positions of high-frequency Raman bands between 1100 and 1800 cm(-1); in particular, a broad mode near 1250 cm(-1) appears only below T-c, attributed to the two-magnon Raman scattering. We also observe weak anomalies in the mode frequencies similar to 100 K due to a magnetically driven ferroelectric phase transition. Understanding of these experimental observations has been possible on the basis of first-principles calculations of the phonons' spectrum and their coupling with spins.

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe-ion direct correlation function and ion-ion dynamic structure factor. Although the power law decay is reminiscent of Debye-Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.