System Size Resonance Associated with Canard Phenomenon in a Biological Cell System

通过研究发现,内噪声对细胞内钙振荡是有影响的,当体系处于由确定性方程所确定的稳定区域时,如果考虑内噪声的作用,就会有随机的钙振荡发生. 并且这种振荡的行为随着体系尺度的变化出现两个最大值,表明了尺度共振现象的发生. 这种行为是与体系的Canard现象密切相关的. 最佳的体系尺度与真实的细胞体积是相吻合的,并且这种吻合基本不随控制参数的改变而改变.     

Fundamental solution of steady oscillations in thermoelastic medium with voids

ABSTRACT

The article deals with the study of plane wave propagation in the thermoelastic medium in the presence of voids. The problem is considered in the context of three-phase-lag model of generalized thermoelasticity. There exists three longitudinal waves, namely elastic (E-mode), thermal (T-mode) and volume fraction (V-mode) in addition to transverse waves which get decoupled from the rest of motion and not affected by thermal and volume fraction fields. The fundamental solution of the system of differential equations in case of steady oscillations in terms of the elementary functions has been constructed. The phase velocity and attenuation coefficient of these waves are computed numerically and presented graphically.     

Oscillation and breakup of a bubble under forced vibration

Coupled shape oscillations and translational motion of an incompressible gas bubble in a vibrating liquid container is studied numerically. The bubble oscillation characteristics are mapped based on the bubble Bond number (Bo) and the ratio of the vibration amplitude of the container to the bubble diameter (A/D). At small Bo and A/D, the bubble oscillation is found to be linear with small amplitudes, and at large Bo and A/D, it is nonlinear and chaotic. This chaotic bubble oscillation is similar to those observed in two coupled nonlinear systems, here being the gas inside the bubble and its surrounding liquid. Further increases in the forcing, results in the bubble breakup due to large liquid inertia.     

Wavelength-independent ultrafast dynamics and coherent oscillation of a metal–carbon stretch vibration in photodissociation of Cr(CO)6 in the region of 270–345 nm

In the group-6 metal hexacarbonyls a number of metal-to-ligand charge-transfer (MLCT) and ligand-field (LF or d → d) states can be excited in the near UV. The latter are repulsive. In equilibrium geometry, most of them are higher than the MLCT states. We probed the dynamics of photodissociation of M(CO)₆ → M(CO)₅ + CO (M = Cr; some data also for M = Mo) with improved time resolution (10–40 fs), pumping at different wavelengths (mainly 270–345 nm) and probing by nonresonant photoionization. The initial relaxation (e.g. within 12.5 fs from T_1u excited at 270 nm) is assigned to direct crossing over to the repulsive surface, from where the subsequent dissociation is also remarkably fast (18 fs in this example). That is, there is no detour via the lowest excited singlet state, in contrast to the usual assumption. Also with 318 and 345 nm excitation a direct MLCT → LF relaxation seems to occur before dissociation. The product M(CO)₅ is generated in the S₁ state, also at pump wavelengths (345 nm) with barely sufficient energy. It relaxes to S₀ through a Jahn–Teller induced conical intersection along pseudorotation coordinates, which stimulates a coherent oscillation in S₀ in this vibration. A higher-frequency oscillation, assigned to totally symmetric MC stretch vibrations, is already found in the Franck–Condon region; it persists (with different wavenumbers) also during dissociation and over the subsequent product states. This vibration is transverse to the valley of dissociation, which is barrierless. The wavelength-independent mechanism also implies that there is no triplet contribution (which was previously supposed at long wavelengths) to photochemical dissociation of the hexacarbonyls.     

Hysteretic behavior induced by an electroacoustic feedback loop in a thermo-acousto-electric generator

An active control method of the spatial distribution of the acoustic field is applied in a thermo-acousto-electric generator. An auxiliary acoustic source is used to force the self-sustained thermoacoustic oscillation in order to control the thermoacoustic amplification. The auxiliary source consists of a loudspeaker, located inside the loop-tube close to the main ambient heat exchanger, and supplied with a delayed signal through an electric feedback loop, comprising a phase-shifter and an amplifier, connected to a reference microphone. Experiments are performed on a prototype engine working with air at a static gauge pressure of 5 bars. Experimental results demonstrate how it is possible to tune the acoustic oscillations in order to increase the global performance of the generator, compared to the case without control, as well as the existence of a hysteretic behavior induced by the electroacoustic feedback loop itself, which leads to a discrepancy between the onset heat input and the offset one.     

A new approach to treating pressure oscillations in combustion instability phenomena

Developing exact models of combustion instabilities is not an easy task to carry out and requires a great deal of time prior to obtaining success. The present study proposes a low-order model for pressure oscillations that does not require any knowledge of the systems, any new physical findings nor intricate details regarding its operating condition. This new approach is obtained using a Modified Van der Pol’s equation (MVDP) which is tuned by use of a Dual Extended Kalman Filter (DKEF) as a recursive estimator with perspectives in control by computer. This phenomenological model is used to predict the pressure signal from a variety of different combustors. Input data were taken from experimental cases such as a Rijke tube, a gas turbine and a liquid-fuel aero-engine combustor. Furthermore, a simulation considering high frequency oscillations to show the capability of the new approach is presented. In all cases, the results demonstrated the feasibility of applying the tractable model MVDP and DKEF running together to investigate pressure oscillations in practical cases.     

奇数阶中立型差分方程的线性化振动性定理

本文得到了奇数阶中立型差分方程的一个线性化振动性定理,是Ｇｙ氹ｒｉ和Ｌａｄａｓ在文［２］中所提公开问题的一个离散结果     

Regular low frequency cardiac output oscillations observed in critically ill surgical patients

A serendipitous finding during development of an automated “electronic flow chart” system to gather data on ICU patients [1] was the observation of low frequency oscillations in blood pressure that were not explained by systematic variability in the environment. [2] This finding has since been confirmed by others. [3,4] In the present report, hemodynamic data for critically ill surgical patients was continuously collected and visualized on a computer workstation to search for patterns not noted by standard monitoring. With this system, we observed low-frequency periodic oscillations in the cardiac output of ten patients, with regular periodicities of 4 to 280 minutes (average = 34 minutes). The mortality rate in these patients was 40%, while the mortality was only 10.8% in 83 similarly monitored intensive care unit (ICU) patients who did not develop regular oscillations in cardiac output. Interestingly, these oscillatory patterns appear to be associated with inadequate resuscitation of increased metabolic rates. The mathematical definition of “chaos” refers to irregular behavior that appears to be random but is actually deterministic. [5] A surprising finding concerning transitions between states of apparent randomness and order in nonlinear systems is that many systems become more organized after being disturbed. Chaotic behavior in biological systems may represent a normal physiologic state, while the loss of chaotic behavior may herald a pathophysiologic state. [6] The mechanism of the regular low frequency oscillations in cardiac output remains to be determined, but the high mortality rate suggests that it is a pathophysiologic marker, perhaps due to inadequate oxygen delivery in under-resuscitated shock. © 1997 John Wiley & Sons, Inc.     

Nonlinear dynamic analysis of a structure with a friction-based seismic base isolation system

Many dynamical systems are subject to some form of non-smooth or discontinuous nonlinearity. One eminent example of such a nonlinearity is friction. This is caused by the fact that friction always opposes the direction of movement, thus changing sign when the sliding velocity changes sign. In this paper, a structure with friction-based seismic base isolation is regarded. Seismic base isolation can be employed to decouple a superstructure from the potentially hazardous surrounding ground motion. As a result, the seismic resistance of the superstructure can be improved. In this case study, the base isolation system is composed of linear laminated rubber bearings and viscous dampers and nonlinear friction elements. The nonlinear dynamic modelling of the base-isolated structure with the aid of constraint equations, is elaborated. Furthermore, the influence of the dynamic characteristics of the superstructure and the nonlinear modelling of the isolation system, on the total system’s dynamic response, is examined. Hereto, the effects of various modelling approaches are considered. Furthermore, the dynamic performance of the system is studied in both nonlinear transient and steady-state analyses. It is shown that, next to (and in correlation with) transient analyses, steady-state analyses can provide valuable insight in the discontinuous dynamic behaviour of the system. This case study illustrates the importance and development of nonlinear modelling and nonlinear analysis tools for non-smooth dynamical systems.