Intermittent chaos in the Bray-Liebhafsky oscillator. Temperature dependence.

Intermittent oscillations as a chaotic mixture of large amplitude relaxation oscillations, grouped in bursts and small-amplitude sinusoidal ones or even quiescent parts between them known as gaps, were found and examined in the Bray-Liebhafsky (BL) reaction performed in CSTR under controlled temperature variations. They were obtained in a narrow temperature range from 61.0 °C to 63.1 °C, where 61.0 °C is the critical temperature for burst emergence from the stable steady state and 63.1 °C is the critical temperature for gap emergence from regular oscillations. Since intermittencies appear gradually from the regular oscillatory state, and no hysteresis was obtained with decreasing/increasing temperature in the vicinity of these two bifurcations, a linear relationship between (τB/τ)(2) and (τG/τ)(2) (where τB, τG and τ denotes duration of bursts, gaps, and whole experiment, respectively), as a function of the temperature as the control parameter, was expected and obtained. Although these intermittent oscillations are chaotic with respect to the lengths of individual gaps as well as bursts, their deterministic behavior related to temperature was additionally established. Thus, the number of bursts or gaps per unit of time (NB/τ and NG/τ) has the form of a normal distribution function over the temperature range in the region where intermittencies are obtained. Temperature dependence of the Lyapunov exponents was also described by a function of the normal distribution form. Hence, we established some regularities in the chaotic behavior of intermittent oscillations that are common in life but difficult for determinations.

Structures of chaos in open reaction systems.

By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.

The chaotic sequences in the Bray-Liebhafsky reaction in an open reactor.

Attractor reconstruction is done from the time series obtained by experimental investigation and by deterministic and stochastic simulation of the Bray-Liebhafsky oscillatory reaction. The appearance of deterministic chaos is confirmed and proven by both simulation and experiment, determining Lyapunov exponents for the sequences of flow rate values, as the control parameter. Moreover, unusual chaotic series were additionally recorded in the experiments, which cannot be found in deterministic numerical simulations. Therefore, an explanation of the difference between the dynamic behavior in the experiment and the deterministic simulation was sought and stochastic simulations based on the same reaction model were particularly useful. The fine structure of the chaotic windows, derived from the analysis of deterministic simulations in the range of flow rate values, made the system highly susceptible to noise induced effects, in general.

Long-term follow-up of Charnley arthroplasty of the hip.

A review of 11.5 year (average interval) follow-up examination of 409 low friction arthroplasties performed included only 3 late failures. The excellent results of the successes have been fully maintained for as long as 14 years. This was true with regard to pain, function of walking and mobility. Resorption of the calcar femorale was rare and no correlation was found with the wear of the socket. The average wear of 1.5 mm was less than predicted by Professor Sir John Charnley. Although 10 patients (7.8%) had excessive wear no patient is at present near the stage of requiring replacement of the socket for this reason. No adverse reaction was found to the implant or the cement.

Postoperative dislocation after Charnley low-friction arthroplasty.

The dislocation rate after the Charnley arthroplasty with the 22 mm diameter femoral head was 0.8% in 3,820 arthroplasties performed before 1971. Over this era the annual rate ranged from 0.5% to 1.4% without any apparent explanation. Following the routine use of a low position for the socket in the acetabulum and the Long Posterior Wall design of socket, the dislocation rate fell to 0.4% over 4,706 arthroplasties and the annual dislocation rate over 4 years ranged between 0.5% and 0.2%.