Effect of gravity on synchronization of two coupled buoyancy-induced turbulent flames.

We study the effect of gravity on the synchronization of two coupled buoyancy-induced turbulent flames by recurrence-based analysis and machine learning. A significant change from nearly complete synchronization in the near field to partial synchronization appears in the far field under low gravity. The synchronized state is gradually lost with increasing gravity level. These results are clearly identified from cross recurrence plots and symbolic recurrence plots and by reservoir computing.

Spatiotemporal dynamics of a buoyancy-driven turbulent fire.

We numerically study the spatiotemporal dynamics and predictability of a buoyancy-driven turbulent fire. A significant transition from order to disorder structures can be observed from the mean degree in the spatial horizontal visibility graph. The gravitational term (baroclinic torque term) in the vorticity equation has a significant impact on the formation of the order (disorder) structure in the near field (far field). The entropy flow transport from temperature to flow velocity fluctuations is predominant near the interface between hot combustion products and ambient air. The transfer entropy is an important measure for determining the predictability of flow velocity fluctuations in the near field obtained by reservoir computing.

Symbolic diffusion entropy rate of chaotic time series as a surrogate measure for the largest Lyapunov exponent.

Existing methods for estimating the largest Lyapunov exponent from a time series rely on the rate of separation of initially nearby trajectories reconstructed from the time series in phase space. According to Ueda, chaotic dynamical behavior is viewed as a manifestation of random transitions between unstable periodic orbits in a chaotic attractor, which are triggered by perturbations due to experimental observation or the roundoff error characteristic of the computing machine, and consequently consists of a sequence of piecewise deterministic processes instead of an entirely deterministic process. Chaotic trajectories might have no physical reality. Here, we propose a mathematical method for estimating a surrogate measure for the largest Lyapunov exponent on the basis of the random diffusion of the symbols generated from a time series in a chaotic attractor, without resorting to initially nearby trajectories. We apply the proposed method to numerical time series generated by chaotic flow models and verify its validity.

Synchronization of two coupled turbulent fires.

We numerically study the scale-free nature of a buoyancy-induced turbulent fire and synchronization of two coupled turbulent fires. A scale-free structure is detected in weighted networks between vortices, while its lifetime obeys a clear power law, indicating intermittent appearances, disappearances, and reappearances of the scale-free property. A significant decrease in the distance between the two fire sources gives rise to a synchronized state in the near field dominated by the unstable motion of transverse vortex rings. The synchronized state vanishes in the far field forming well-developed turbulent plumes, regardless of the distance between the two fire sources.

Estimation of the degree of dynamical instability from the information entropy of symbolic dynamics.

A positive Lyapunov exponent is the most convincing signature of chaos. However, existing methods for estimating the Lyapunov exponent from a time series often give unreliable estimates because they trace the time evolution of the distance between a pair of initially neighboring trajectories in phase space. Here, we propose a mathematical method for estimating the degree of dynamical instability, as a surrogate for the Lyapunov exponent, without tracing initially neighboring trajectories on the basis of the information entropy from a symbolic time series. We apply the proposed method to numerical time series generated by well-known chaotic systems and experimental time series and verify its validity.

Nonlinear dynamics of a buoyancy-induced turbulent fire.

We conduct a numerical study on the dynamic behavior of a buoyancy-induced turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. Here, we consider two classes of entropies: the permutation entropy and network entropy in ε-recurrence networks, both of which evaluate the degree of randomness in the underlying dynamics. These entropies enable us to capture the significant changes in the dynamic behavior of flow velocity fluctuations. The possible presence of two important dynamics, low-dimensional deterministic chaos in the near field dominated by the motion of large-scale vortices and high-dimensional chaos in the far field forming a well-developed turbulent plume, is clearly identified by the multiscale complexity-entropy causality plane.

Chaotic gas turbine subject to augmented Lorenz equations.

Inspired by the chaotic waterwheel invented by Malkus and Howard about 40 years ago, we have developed a gas turbine that randomly switches the sense of rotation between clockwise and counterclockwise. The nondimensionalized expressions for the equations of motion of our turbine are represented as a starlike network of many Lorenz subsystems sharing the angular velocity of the turbine rotor as the central node, referred to as augmented Lorenz equations. We show qualitative similarities between the statistical properties of the angular velocity of the turbine rotor and the velocity field of large-scale wind in turbulent Rayleigh-Bénard convection reported by Sreenivasan et al. [Phys. Rev. E 65, 056306 (2002)]. Our equations of motion achieve the random reversal of the turbine rotor through the stochastic resonance of the angular velocity in a double-well potential and the force applied by rapidly oscillating fields. These results suggest that the augmented Lorenz model is applicable as a dynamical model for the random reversal of turbulent large-scale wind through cessation.

Short-term prediction of dynamical behavior of flame front instability induced by radiative heat loss.

We apply nonlinear forecasting to the time series of the flame front instability induced by radiative heat loss to test for the short-term predictability and long-term unpredictability characteristic of deterministic chaos in flame front instability. Our results indicate that the flame front instability represents high-dimensional chaos generated via the period-doubling cascade process reported in our previous study [H. Gotoda, K. Michigami, K. Ikeda, and T. Miyano, Combust Theory Modell. 14, 479 (2010)], while its short-term behavior is predictable using a local nonlinear predictor based on the Sugihara-May method [H. Gotoda, H. Nikimoto, T. Miyano, and S. Tachibana, Chaos 20, 013124 (2011); G. Sugihara and R. M. May, Nature 344, 734 (1990)] as well as a generalized radial basis function network as a global nonlinear predictor. The feasibility of a new approach based on short-term prediction is also discussed in this work from the practical viewpoint of combustion systems.

Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor.

We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout.

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor.

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.

Dynamic properties of unstable motion of swirling premixed flames generated by a change in gravitational orientation.

The dynamic behavior of swirling premixed flames generated by the effect of the gravitational orientation has been experimentally and numerically investigated. When the gravitational direction relative to the flame front is changed, i.e., in inverted gravity (-1G), an unstable flame is formed in a limited domain of equivalence ratio and swirl number. The time history of flame front fluctuation shows that high-energy chaotic motion is superimposed on a periodic oscillation generated by unstable vortex motion in the combustion products. This results in the dynamic motion of the unstable flame becoming deterministically chaotic. This is clearly demonstrated by sophisticated nonlinear time series analysis, which has not been widely applied to the investigation of combustion phenomena.

Collective synchronization as a method of learning and generalization from sparse data.

We propose a method for extracting general features from multivariate data using a network of phase oscillators subject to an analogue of the Kuramoto model for collective synchronization. In this method, the natural frequencies of the oscillators are extended to vector quantities to which multivariate data are assigned. The common frequency vectors of the groups of partially synchronized oscillators are interpreted to be the template vectors representing the general features of the data set. We show that the proposed method becomes equivalent to the self-organizing map algorithm devised by Kohonen when the governing equations are linearized about their solutions of partial synchronization. As a case study to test the utility of our method, we applied it to care-needs-certification data in the Japanese public long-term care insurance program, and found major general patterns in the health status of the elderly needing nursing care.

Data synchronization in a network of coupled phase oscillators.

We devised a new method of data mining for a large-scale database. In the method, a network of locally coupled phase oscillators subject to Kuramoto's model substitutes for given multivariate data to generate major features through phase locking of the oscillators, i.e., phase transition of the data set. We applied the method to the national database of care needs certification for the Japanese public long-term care insurance program, and found three major patterns in the aging process of the frail elderly. This work revealed the latent utility of Kuramoto's model for data processing.

Prediction of care class by local additive reference to prototypical examples.

The public long-term care insurance program for the elderly in Japan set out in 2000 toward establishing a new system whereby citizens can be assured that they will receive care and be supported by the society as a whole. The insurance program includes computer-aided certification processes to estimate the needs for nursing care for clients. In this work, we show the applicability of an adaptive local nonlinear approximation method associated with the Japanese national database for automatic inference of the care class.

Sugar micro needles as transdermic drug delivery system.

We designed and fabricated an array of sugar micro needles of the length ranging from 150 micro m to 2 mm for transdermic delivery of drugs. Micro needles were molded out of maltose mixed with pharmaceutical material, being expected bio-degradable in the human skin. To test basic tolerance to the healthy human skin, a clinical experiment was carried out for 10 healthy adult volunteers. 500 microm-needles containing 5 wt% of ascorbate-2-glycoside were inserted into the skin of the forearm and snapped off to be left in the skin. They spontaneously dissolved by hydrolysis to release ascorbate in the epidermis and the dermis. No dermatological problems were observed in terms of the International Contact Dermatitis Research Group criteria. These observations indicate that the present system is a novel approach to achieve transdermic drug delivery.