Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length

A study was conducted on the dynamics of 2D and 3D Bose-Einstein condensates in the case when the scattering length in the Gross-Pitaevskii (GP) equation which contains constant (dc) and time-variable (ac) parts. Using the variational approximation (VA), simulating the GP equation directly, and applying the averaging procedure to the GP equation without the use of the VA, it was demonstrated that the ac component of the nonlinearity makes it possible to maintain the condensate in a stable self-confined state without external traps.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Sensitivity of AMPA receptor channel to calcium oscillations: A computational study

We used a computational model of biochemical pathways that are involved in the phosphorylation/dephosphorylation of AMPA receptor to study the receptor responses to calcium oscillations. In the model, the biochemical pathways are assumed to be located immediately under the postsynaptic membrane and we included three states of AMPA receptor: dephosphorylated, and phosphorylated in one or in two sites. To characterize the effects of calcium oscillations on the AMPA receptor, we exposed the model to stimuli with three varying parameters, namely frequency, number of pulses and calcium spike duration. Our model showed sensitivity to all of these three parameters. © 2002 Elsevier Science B.V. All rights reserved.

An active leakage-injection scheme applied to low-voltage SRAMs

An active leakage-injection scheme (ALIS) for low-voltage (LV) high-density (HD) SRAMs is presented. By means of a feedback loop comprising a servo-amplifier and a common-drain MOSFET, a current matching the respective bit-line leakage is injected onto the line during precharge and sensing, preventing the respective capacitances from erroneous discharges. The technique is able to handle leakages up to hundreds of μA at high operating temperatures. Since no additional timing is required, read-out operations are performed at no speed penalty. A simplified 256×1bit array was designed in accordance with a 0.35 CMOS process and 1.2V-supply. A range of PSPICE simulation attests the efficacy of ALIS. With an extra power consumption of 242 μW, a 200 μA-leakage @125°C, corresponding to 13.6 times the cell current, is compensated.

A Short Note on a Nonlinear System vibrations under Two Non-Ideal Excitations

This paper describes a nonlinear phenomenon in the dynamical behavior of a nonlinear system under two non-ideal excitations: the self-synchronization of unbalanced direct current motors. The considered model is taken as a Duffing system that is excited by two unbalanced direct current motors with limited power supplies. The results obtained by using numerical simulations are discussed in details.

Analysis of a sub-optimal scheme of drug dosage in the AIDS treatment

Here the results for CD4+T cells count and the viral load obtained from HIV sero-positive patients are compared with results from numerical simulations by computer. Also, the standard scheme of administration of drugs anti HIV (HAART schemes) which uses constant doses is compared with an alternative sub-optimal teatment scheme which uses variable drug dosage according to the evolution of a quantitative measure of the side effects. The quantitative analysis done here shows that it is possible to obtain, using the alternative scheme, the same performance of actual data but using variable dosage and having fewer side effects. Optimal control theory is used to solve and also to provide a prognosis related to the strategies for control of viraemia.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

Modal Analysis of a Beam with a Tip Rotor by Using a Fundamental Response

The shape modes of a damped-free beam model with a tip rotor are determined by using a dynamical basis that is generated by a fundamental spatial free response. This is a non-classical distributed model for the displacements in the transverse directions of the beam which turns out to be coupled through boundary conditions due to rotation. Numerical calculations are performed by using the Ritz-Rayleigh method with several approximating basis.

On Nonlinear Dynamics and Control of A Particular Portal Frame Foundation Model, Excited by a Non-Ideal Motor

The nonlinear dynamic response and a nonlinear control method of a particular portal frame foundation for an unbalanced rotating machine with limited power (non-ideal motor) are examined. Numerical simulations are performed for a set of control parameters (depending on the voltage of the motor) related to the static and dynamic characteristics of the motor. The interaction of the structure with the excitation source may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. A mathematical model having two degrees of freedom simplifies the non-ideal system. The study of controlling steady-state vibrations of the non-ideal system is based on the saturation phenomenon due to internal resonance.

Mean-field model of jet formation in a collapsing Bose-Einstein condensate

We perform a systematic numerical study, based on the time-dependent Gross-Pitaevskii equation, of jet formation in collapsing and exploding Bose-Einstein condensates as in the experiment by Donley et al (2001 Nature 412 295). In the actual experiment, via a Feshbach resonance, the scattering length of atomic interaction was suddenly changed from positive to negative on a pre-formed condensate. Consequently, the condensate collapsed and ejected atoms via explosion. On disruption of the collapse by suddenly changing the scattering length to zero, a radial jet of atoms was formed in the experiment. We present a satisfactory account of jet formation under the experimental conditions and also make predictions beyond experimental conditions which can be verified in future experiments.

Antioxidant activity of flavonols

In this work we use a single new electronic index to describe the antioxidant activity of the flavonols, a special class of flavonoids. We also try to predict theoretically the antioxidant activity of some yet nonisolated flavonols. © 2003 Wiley Periodicals, Inc.

On designing linearly tunable high-Q OTA-C filters with low sensitivity

This paper discusses a design approach for a high-Q low-sensitivity OTA-C biquad bandpass section. An optimal relationship is established between transconductances defining the differenceβ - γ in the Q-factor denominator, setting the Q-sensitivity to tuning voltages around unity. A 30-MHz filter was designed based on a 0.35μn CMOS process and VDD=3.3V. A range of circuit simulation supports the theoretical analysis. Q-factor spans from 20.5 to 60, while ensuring filter stability along the tuning range. Although a Mode-operating OTA is used, the procedure can be extended to other types of transconductor.

A low-voltage low-sensitivity sinusoidal VCO for DPLL realizations

A quasi-sinusoidal linearly tunable OTA-C VCO built with triode-region transconductors is presented. Oscillation upon power-on is ensured by RHP poles associated with gate-drain capacitances of OTA input devices. Since the OTA nonlinearity stabilizes the amplitude, the oscillation frequency f0 is first-order independent of VDD, making the VCO adequate to mixed-mode designs. A range of simulations attests the theoretical analysis. As part of a DPLL, the VCO was prototyped on a 0.8μm CMOS process, occupying an area of 0.15mm2. Nominal f0 is 1MHz, with K VCo=8.4KHz/mV. Measured sensitivity to VDD is below 2.17, while phase noise is -86dBc at 100-KHz offset. The feasibility of the VCO for higher frequencies is verified by a redesign based on a 0.35μm CMOS process and VDD=3.3V, with a linear frequency-span of l3.2MHz - 61.5MHz.

Precision of yule-walker methods for the arma spectral model

In this work a new method is proposed of separated estimation for the ARMA spectral model based on the modified Yule-Walker equations and on the least squares method. The proposal of the new method consists of performing an AR filtering in the random process generated obtaining a new random estimate, which will reestimate the ARMA model parameters, given a better spectrum estimate. Some numerical examples will be presented in order to ilustrate the performance of the method proposed, which is evaluated by the relative error and the average variation coefficient.