Robustness and Coherence of a Three-Protein Circadian Oscillator: Landscape and Flux Perspectives

Three-protein circadian oscillations in cyanobacteria sustain for weeks. To understand how cellular oscillations function robustly in stochastic fluctuating environments, we used a stochastic model to uncover two natures of circadian oscillation: the potential landscape related to steady-state probability distribution of protein concentrations; and the corresponding flux related to speed of concentration changes which drive the oscillations. The barrier height of escaping from the oscillation attractor on the landscape provides a quantitative measure of the robustness and coherence for oscillations against intrinsic and external fluctuations. The difference between the locations of the zero total driving force and the extremal of the potential provides a possible experimental probe and quantification of the force from curl flux. These results, correlated with experiments, can help in the design of robust oscillatory networks.

MEASUREMENT AND CALCULATION OF SPONTANEOUS EMISSION BRANCHING RATIOS, RELATIVE OSCILLATOR-STRENGTHS, TRANSITION-PROBABILITIES AND LEVEL LIFETIMES FOR ATOMIC URANIUM

We propose a laser induced sensitized fluorescence spectrometry for measuring the spontaneous emission branching ratios o?the transitions from the ten levels 5f36d7s7p-7M7, 5f36d7s7p-7L6, 5f37s27p-5K6, 5f26d27s2 - 5L7, 5f46d7s - 7L6, (17,070cm-1)-5L6, 5f26d27s2-5K6, 6d7s7p-7L5, 5f36d7s7p-7K5 and 5f26d27s2-5I5 to the ground state of atomic uranium (UI) for the first time. Their relative oscillator strengths have been measured by means of hollow cathode discharge (HCD) emission spectrometry. The radiative...

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

Synchronous chaos in the coupled system of two logistic maps

Synchronous chaos is investigated in the coupled system of two Logistic maps. Although the diffusive coupling admits all synchronized motions, the stabilities of their configurations are dependent on the transverse Lyapunov exponents while independent of the longitudinal Lyapunov exponents. It is shown that synchronous chaos is structurally stable with respect to the system parameters. The mean motion is the pseudo-orbit of an individual local map so that its dynamics can be described by the local map. (C) 2004 Elsevier Ltd. All rights reserved.

Variation of added mass and its application to the calculation of amplitude response for a circular cylinder

In the present study, analyzed are the variation of added mass for a circular cylinder in the lock-in ( synchronization) range of vortex-induced vibration (VIV) and the relationship between added mass and natural frequency. A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given. Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio. A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a circular cylinder at lock-in are better than the ideal added mass. In addition, computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Nonlinear Fluid Damping In Structure-Wake Oscillators In Modeling Vortex-Induced Vibrations

A Nonlinear Fluid Damping (NFD) in the form of the square-velocity is applied in the response analysis of Vortex-induced Vibrations (VIV). Its nonlinear hydrodynamic effects oil the coupled wake and structure oscillators are investigated. A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics, such as the amplification of body displacement at lock-in and frequency lock-ill, both at high and low mass ratios. Particularly, the predicted peak amplitude of the body in the Griffin plot is ill good agreement with experimental data and empirical equation, indicating the significant effect of the NFD on the structure motion.

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.

Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping

A Nd:glass regenerative amplifier has been set up to generate the pumping pulse with variable pulse width for an optical parametric chirped-pulse amplification (OPCPA) laser system. Each pulse of the pulse train from a cw self-mode-locking femtosecond Ti:sapphire oscillator is stretched to approximate to300 ps at 1062 nm to be split equally and injected into a nonlinear crystal and the Nd:glass regenerative amplifier, as the chirped signal pulse train and the seed pulse train of the pumping laser system, respectively. By adjusting the cavity length of the regenerative amplifier directly, the width of amplified pulse could be varied continuously from approximate to300 ps to approximate to3 ns. The chirped signal pulse for the OPCPA laser system and the seed pulse for the pumping laser system come from the same oscillator, so that the time jitter between the signal pulse and the pumping pulse in optical parametric amplification stages could be <10 ps. (C) 2003 Society of Photo-Optical Instrumentation Engineers.

High-conversion-efficiency and broadband tunable femtosecond noncollinear optical parametric amplifier

We build a compact high-conversion-efficiency and broadband tunable noncollinear optical parametric amplifier (OPA) in the infra-red (IR) pumped by a femtosecond Ti:sapphire CPA laser. The OPA consists of an internal seed of white-light continuum generator (WLG) and two noncollinear optical parametric amplifiers. The tunable wavelength range is from 1.2 mu m to 2.4 mu m for both signal and idle pulses. The total OPA efficiency in the last OPA stage reaches about 40% in a wider tunable spectral range (from 1.3 mu m to 1.7 mu m for signal pulse, from 1.5 mu m to 2.0 mu m for idle pulse respectively).

Laser-driven coherent betatron oscillation in a laser-wakefield cavity

The origin of beam disparity in emittance and betatron oscillation orbits, in and out of the polarization plane of the drive laser of laser-plasma accelerators, is explained in terms of betatron oscillations driven by the laser field. As trapped electrons accelerate, they move forward and interact with the laser pulse. For the bubble regime, a simple model is presented to describe this interaction in terms of a harmonic oscillator with a driving force from the laser and a restoring force from the plasma wake field. The resulting beam oscillations in the polarization plane, with period approximately the wavelength of the driving laser, increase emittance in that plane and cause microbunching of the beam. These effects are observed directly in 3D particle-in-cell simulations.

Propagation of a few-cycle laser pulse in a V-type three-level system

Propagation of a few-cycle laser pulse in a V-type three-level system (fine structure levels of rubidium) is investigated numerically. The full three-level Maxwell-Bloch equations without the rotating wave approximation and the standing slowly varying envelope approximation are solved by using a finite-difference time-domain method. It is shown that, when the usual unequal oscillator strengths are considered, self-induced transparency cannot be recovered and higher spectral components can be produced even for small-area pulses. (c) 2005 Pleiades Publishing, Inc.